Atkin-Lehner |
2+ 7+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614d |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
154368 |
Modular degree for the optimal curve |
Δ |
626585243648 = 212 · 74 · 133 · 29 |
Discriminant |
Eigenvalues |
2+ -2 0 7+ 4 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-18581,-975648] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:63:1] [10100:5747:64] |
Generators of the group modulo torsion |
j |
322899450545125/285200384 |
j-invariant |
L |
5.7696363337633 |
L(r)(E,1)/r! |
Ω |
0.40893860583727 |
Real period |
R |
7.054404073663 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999486 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68614z1 |
Quadratic twists by: 13 |