Atkin-Lehner |
2+ 5- 29+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
15370d |
Isogeny class |
Conductor |
15370 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
12160 |
Modular degree for the optimal curve |
Δ |
-1229600000 = -1 · 28 · 55 · 29 · 53 |
Discriminant |
Eigenvalues |
2+ -1 5- -3 -3 0 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-3587,81229] |
[a1,a2,a3,a4,a6] |
Generators |
[-67:196:1] [38:-59:1] |
Generators of the group modulo torsion |
j |
-5106308007036601/1229600000 |
j-invariant |
L |
4.2990805050781 |
L(r)(E,1)/r! |
Ω |
1.4961835626648 |
Real period |
R |
0.28733643466995 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122960m1 76850h1 |
Quadratic twists by: -4 5 |