Atkin-Lehner |
2+ 3+ 7- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69384f |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
38799004523129424 = 24 · 35 · 77 · 594 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 4 -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-84639,-97236] |
[a1,a2,a3,a4,a6] |
Generators |
[9875:980833:1] |
Generators of the group modulo torsion |
j |
35623139473408/20611631061 |
j-invariant |
L |
3.9483120518843 |
L(r)(E,1)/r! |
Ω |
0.30692020334633 |
Real period |
R |
6.4321475250175 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980251 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
9912f1 |
Quadratic twists by: -7 |