Properties

Label 466752.e
Number of curves $1$
Conductor $466752$
CM no
Rank $1$

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

Elliptic curves in class 466752.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.e1 466752e1 \([0, -1, 0, -3550515, -2573864919]\) \(-77342448315065684437504/40814262224307\) \(-2612112782355648\) \([]\) \(10386432\) \(2.2887\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 466752.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 466752.e do not have complex multiplication.

Modular form 466752.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + q^{7} + q^{9} - q^{11} + q^{13} + 4 q^{15} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display