TY - JOUR

T1 - Bielliptic modular curves X0* (n) with square-free levels

AU - Bars, Francesc

AU - Rovira, Josep González

PY - 2019/1/1

Y1 - 2019/1/1

N2 - © 2019 American Mathematical Society. Let N ≥ 1 be a square-free integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 19 values of N, and we determine the automorphism group of these bielliptic curves. In particular, we obtain the first examples of nontrivial Aut(X0* (N)) when the genus of X0* (N) is ≥ 3. Moreover, we prove that the set of all quadratic points over ℚ for the modular curve X0* (N) with genus ≥ 2 and N square-free is not finite exactly for 51 values of N.

AB - © 2019 American Mathematical Society. Let N ≥ 1 be a square-free integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 19 values of N, and we determine the automorphism group of these bielliptic curves. In particular, we obtain the first examples of nontrivial Aut(X0* (N)) when the genus of X0* (N) is ≥ 3. Moreover, we prove that the set of all quadratic points over ℚ for the modular curve X0* (N) with genus ≥ 2 and N square-free is not finite exactly for 51 values of N.

U2 - https://doi.org/10.1090/mcom/3424

DO - https://doi.org/10.1090/mcom/3424

M3 - Article

VL - 88

SP - 2939

EP - 2957

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

ER -