Atkin-Lehner |
2- 7+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
61712f |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
319488 |
Modular degree for the optimal curve |
Δ |
-637917366603776 = -1 · 212 · 72 · 194 · 293 |
Discriminant |
Eigenvalues |
2- 1 -3 7+ 5 3 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-69312,-7151116] |
[a1,a2,a3,a4,a6] |
Generators |
[10812:146566:27] |
Generators of the group modulo torsion |
j |
-8990737580405953/155741544581 |
j-invariant |
L |
5.8468551927216 |
L(r)(E,1)/r! |
Ω |
0.14696719865281 |
Real period |
R |
1.6576417635766 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000026 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3857b1 |
Quadratic twists by: -4 |