Properties

Label 6960.u
Number of curves 11
Conductor 69606960
CM no
Rank 00

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Show commands: SageMath
Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Elliptic curves in class 6960.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6960.u1 6960bd1 [0,1,0,190,1025][0, -1, 0, -190, -1025] 47659369216/4404375-47659369216/4404375 70470000-70470000 [][] 19201920 0.248390.24839 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 6960.u1 has rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
331+T1 + T
551T1 - T
29291T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 13T+7T2 1 - 3 T + 7 T^{2} 1.7.ad
1111 13T+11T2 1 - 3 T + 11 T^{2} 1.11.ad
1313 1T+13T2 1 - T + 13 T^{2} 1.13.ab
1717 1+3T+17T2 1 + 3 T + 17 T^{2} 1.17.d
1919 16T+19T2 1 - 6 T + 19 T^{2} 1.19.ag
2323 14T+23T2 1 - 4 T + 23 T^{2} 1.23.ae
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 6960.u do not have complex multiplication.

Modular form 6960.2.a.u

Copy content sage:E.q_eigenform(10)
 
qq3+q5+3q7+q9+3q11+q13q153q17+6q19+O(q20)q - q^{3} + q^{5} + 3 q^{7} + q^{9} + 3 q^{11} + q^{13} - q^{15} - 3 q^{17} + 6 q^{19} + O(q^{20}) Copy content Toggle raw display