Atkin-Lehner |
2- 7- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
86632r |
Isogeny class |
Conductor |
86632 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
157132800 |
Modular degree for the optimal curve |
Δ |
-549613565370198784 = -1 · 28 · 711 · 13 · 174 |
Discriminant |
Eigenvalues |
2- 2 -1 7- 0 13+ 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-313300389761,-67497679794008491] |
[a1,a2,a3,a4,a6] |
Generators |
[211984830475943369099826683050256076442950510341889516526268920330062531952442490215901458982000187220262601968455014555228159017770425080431961698522562084904898296589814012150753781111990597114643403109777059608026069017325:382371050641209130241170483747680517410323031851375935787330805543547137591647822121759196599404125461512727793796054608058986413454719686058839344373868349195710170929609328187637265200528463552565328212489900268005695546276646:63222149678223750813702517420827585393460682958494710977247848703879267216216468705370615825459046550216755365894716561431338692876496360247113828069836989316010715961617195574302523879996526028696888480430291794389407] |
Generators of the group modulo torsion |
j |
-112921935191145358638804243137536/18248586811 |
j-invariant |
L |
8.7802075274427 |
L(r)(E,1)/r! |
Ω |
0.0031906511650024 |
Real period |
R |
343.98180314064 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12376j1 |
Quadratic twists by: -7 |