Properties

Label 4140.e
Number of curves 11
Conductor 41404140
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4140.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4140.e1 4140k1 [0,0,0,6902448,3048337996][0, 0, 0, 6902448, -3048337996] 194879272239195815936/134287459716796875194879272239195815936/134287459716796875 25061262882187500000000-25061262882187500000000 [][] 349440349440 2.98662.9866 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4140.e1 has rank 11.

Complex multiplication

The elliptic curves in class 4140.e do not have complex multiplication.

Modular form 4140.2.a.e

sage: E.q_eigenform(10)
 
q+q55q7+4q13+3q174q19+O(q20)q + q^{5} - 5 q^{7} + 4 q^{13} + 3 q^{17} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display