Atkin-Lehner |
3+ 5+ 7- 41- |
Signs for the Atkin-Lehner involutions |
Class |
12915a |
Isogeny class |
Conductor |
12915 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-197715735 = -1 · 39 · 5 · 72 · 41 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- -4 -2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,52,-674] |
[a1,a2,a3,a4,a6] |
Generators |
[8:10:1] |
Generators of the group modulo torsion |
j |
804357/10045 |
j-invariant |
L |
2.3538525903388 |
L(r)(E,1)/r! |
Ω |
0.87748298077079 |
Real period |
R |
2.6825051219468 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12915b1 64575d1 90405f1 |
Quadratic twists by: -3 5 -7 |