Analytic rank: | 1 |
Mordell-Weil rank: | 1 |
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+2T2 |
3 | 1 |
5 | 1+5T2 |
|
|
Good L-factors: |
Prime |
L-Factor |
7 | 1+7T2+49T4 |
11 | (1−3T+11T2)(1+3T+11T2) |
13 | (1−2T+13T2)(1+5T+13T2) |
17 | (1+17T2)2 |
19 | 1+2T−15T2+38T3+361T4 |
23 | 1+19T2+529T4 |
29 | (1−6T+29T2)(1+6T+29T2) |
⋯ | ⋯ |
|
|
See L-function page for more information |
ST= J(E6), ST0=SU(2)
Splits over the number field Q(b)≃ 6.2.450000.1 with defining polynomial:
x6−x5−5x3−x+1
Decomposes up to isogeny as the product of the non-isogenous elliptic curve isogeny classes:
y2=x3−g4/48x−g6/864 with
g4=192b5−690b4+690b3−750b2+2280b−672
g6=−20160b5+10080b4+20160b3+80640b2+40320b−39060
Conductor norm: 4782969
y2=x3−g4/48x−g6/864 with
g4=−192b5−210b4+210b3+1650b2+1320b+672
g6=20160b5−10080b4−20160b3−80640b2−40320b−28980
Conductor norm: 4782969
Not of GL2-type over Q
Endomorphism algebra over Q:
End(J)⊗Q | ≃ | Q |
End(J)⊗R | ≃ | R |
Smallest field over which all endomorphisms are defined:
Galois number field K=Q(a) with defining polynomial x12−x11+x10+10x9−5x8−x7+26x6−x5−5x4+10x3+x2−x+1
Endomorphism algebra over Q:
End(JQ)⊗Q | ≃ | M2(Q) |
End(JQ)⊗R | ≃ | M2(R) |
More complete information on endomorphism algebras and rings can be found on the pages of the individual curves in the isogeny class.