Atkin-Lehner |
2+ 3- 5+ 7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
51240i |
Isogeny class |
Conductor |
51240 |
Conductor |
∏ cp |
400 |
Product of Tamagawa factors cp |
deg |
339200 |
Modular degree for the optimal curve |
Δ |
-387447226387200 = -1 · 28 · 310 · 52 · 75 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -6 -6 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-101081,12372075] |
[a1,a2,a3,a4,a6] |
Generators |
[-338:2835:1] [607:13230:1] |
Generators of the group modulo torsion |
j |
-446166165132012544/1513465728075 |
j-invariant |
L |
10.443105227108 |
L(r)(E,1)/r! |
Ω |
0.53668048235853 |
Real period |
R |
0.048646753377421 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102480d1 |
Quadratic twists by: -4 |