Atkin-Lehner |
2+ 3+ 5+ 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
51150l |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192000 |
Modular degree for the optimal curve |
Δ |
-129473437500000 = -1 · 25 · 35 · 511 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -3 11- 1 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9625,653125] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:950:1] |
Generators of the group modulo torsion |
j |
-6312136778641/8286300000 |
j-invariant |
L |
2.8565467303673 |
L(r)(E,1)/r! |
Ω |
0.52845181748562 |
Real period |
R |
1.3513752038708 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000019 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10230bh1 |
Quadratic twists by: 5 |