Atkin-Lehner |
2- 3+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
7812b |
Isogeny class |
Conductor |
7812 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
-20342448 = -1 · 24 · 33 · 72 · 312 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -6 -2 -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-216,1241] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:49:1] [4:21:1] |
Generators of the group modulo torsion |
j |
-2579890176/47089 |
j-invariant |
L |
4.8956382564234 |
L(r)(E,1)/r! |
Ω |
2.1629340343919 |
Real period |
R |
0.37723744526187 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31248be1 124992e1 7812a1 54684e1 |
Quadratic twists by: -4 8 -3 -7 |