Atkin-Lehner |
2- 3- 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
61380p |
Isogeny class |
Conductor |
61380 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-40954219892190000 = -1 · 24 · 318 · 54 · 11 · 312 |
Discriminant |
Eigenvalues |
2- 3- 5- 2 11+ -4 -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-47172,10504861] |
[a1,a2,a3,a4,a6] |
Generators |
[207:3100:1] |
Generators of the group modulo torsion |
j |
-995242860396544/3511164256875 |
j-invariant |
L |
6.4913856074594 |
L(r)(E,1)/r! |
Ω |
0.31731710737712 |
Real period |
R |
2.5571366373018 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000194 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20460j1 |
Quadratic twists by: -3 |