Properties

Label 8640.u
Number of curves 11
Conductor 86408640
CM no
Rank 11

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

Elliptic curves in class 8640.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8640.u1 8640bv1 [0,0,0,108,8208][0, 0, 0, -108, -8208] 24/5-24/5 29023764480-29023764480 [][] 57605760 0.686900.68690 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8640.u1 has rank 11.

Complex multiplication

The elliptic curves in class 8640.u do not have complex multiplication.

Modular form 8640.2.a.u

sage: E.q_eigenform(10)
 
qq5+2q73q11+5q133q17+O(q20)q - q^{5} + 2 q^{7} - 3 q^{11} + 5 q^{13} - 3 q^{17} + O(q^{20}) Copy content Toggle raw display