Atkin-Lehner |
2+ 3+ 7- 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
119658n |
Isogeny class |
Conductor |
119658 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-3940839362541312 = -1 · 28 · 38 · 78 · 11 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11+ -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-809,-3020667] |
[a1,a2,a3,a4,a6] |
Generators |
[2820982480:-210824222669:512000] |
Generators of the group modulo torsion |
j |
-498677257/33496581888 |
j-invariant |
L |
5.3323885299474 |
L(r)(E,1)/r! |
Ω |
0.20120006713764 |
Real period |
R |
13.251458069444 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000043995 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17094k1 |
Quadratic twists by: -7 |