Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ej |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
177408 |
Modular degree for the optimal curve |
Δ |
-44819869710528 = -1 · 26 · 33 · 1110 |
Discriminant |
Eigenvalues |
2- 3+ 0 5 11- 2 0 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,0,322102] |
[a1,a2,a3,a4,a6] |
Generators |
[32837:375663:343] |
Generators of the group modulo torsion |
j |
0 |
j-invariant |
L |
8.5030497299131 |
L(r)(E,1)/r! |
Ω |
0.50807376653181 |
Real period |
R |
8.3679283298907 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000754 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696q1 17424bf1 69696ej2 69696ek1 |
Quadratic twists by: -4 8 -3 -11 |