Atkin-Lehner |
3- 5+ 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
31005m |
Isogeny class |
Conductor |
31005 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-4644420336516796875 = -1 · 37 · 58 · 13 · 535 |
Discriminant |
Eigenvalues |
-2 3- 5+ -2 1 13+ -4 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-613443,-212015102] |
[a1,a2,a3,a4,a6] |
Generators |
[9191:877812:1] |
Generators of the group modulo torsion |
j |
-35020216697719361536/6370946963671875 |
j-invariant |
L |
2.0134510834429 |
L(r)(E,1)/r! |
Ω |
0.084460336461539 |
Real period |
R |
1.1919506645346 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10335d1 |
Quadratic twists by: -3 |