Atkin-Lehner |
3+ 5+ 7- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
69615b |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
157440 |
Modular degree for the optimal curve |
Δ |
-32638166071875 = -1 · 39 · 55 · 74 · 13 · 17 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7- 6 13+ 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,7452,-119347] |
[a1,a2,a3,a4,a6] |
Generators |
[69:850:1] |
Generators of the group modulo torsion |
j |
2325149908992/1658190625 |
j-invariant |
L |
5.1912815680593 |
L(r)(E,1)/r! |
Ω |
0.36980258354933 |
Real period |
R |
1.7547476001402 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999783 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69615d1 |
Quadratic twists by: -3 |