Properties

Label 346560.s
Number of curves 11
Conductor 346560346560
CM no
Rank 11

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Show commands: SageMath
Copy content sage:E = EllipticCurve("s1") E.isogeny_class()
 

Elliptic curves in class 346560.s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.s1 346560s1 [0,1,0,11311,307465][0, -1, 0, -11311, 307465] 19189812736/632812519189812736/6328125 5278000500000052780005000000 [][] 838656838656 1.33601.3360 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 346560.s1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
331+T1 + T
551+T1 + T
191911
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 1+2T+7T2 1 + 2 T + 7 T^{2} 1.7.c
1111 1+T+11T2 1 + T + 11 T^{2} 1.11.b
1313 1+13T2 1 + 13 T^{2} 1.13.a
1717 16T+17T2 1 - 6 T + 17 T^{2} 1.17.ag
2323 1+6T+23T2 1 + 6 T + 23 T^{2} 1.23.g
2929 13T+29T2 1 - 3 T + 29 T^{2} 1.29.ad
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 346560.s do not have complex multiplication.

Modular form 346560.2.a.s

Copy content sage:E.q_eigenform(10)
 
qq3q52q7+q9q11+q15+6q17+O(q20)q - q^{3} - q^{5} - 2 q^{7} + q^{9} - q^{11} + q^{15} + 6 q^{17} + O(q^{20}) Copy content Toggle raw display