Atkin-Lehner |
2+ 3+ 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970d |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
878592 |
Modular degree for the optimal curve |
Δ |
-7507019499724800 = -1 · 213 · 32 · 52 · 118 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 3 11- 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-331058,-73573452] |
[a1,a2,a3,a4,a6] |
j |
-18719599019209/35020800 |
j-invariant |
L |
1.5920791502551 |
L(r)(E,1)/r! |
Ω |
0.099504947554012 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970br1 |
Quadratic twists by: -11 |