Properties

Label 270504.e
Number of curves 11
Conductor 270504270504
CM no
Rank 11

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

Elliptic curves in class 270504.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270504.e1 270504e1 [0,0,0,41259,3225206][0, 0, 0, -41259, 3225206] 36004308772/659136004308772/6591 14219248343041421924834304 [][] 580608580608 1.33491.3349 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 270504.e1 has rank 11.

Complex multiplication

The elliptic curves in class 270504.e do not have complex multiplication.

Modular form 270504.2.a.e

sage: E.q_eigenform(10)
 
q3q5+q72q11q13q19+O(q20)q - 3 q^{5} + q^{7} - 2 q^{11} - q^{13} - q^{19} + O(q^{20}) Copy content Toggle raw display