Properties

Label 458640gm
Number of curves $1$
Conductor $458640$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gm1")
 
E.isogeny_class()
 

Elliptic curves in class 458640gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.gm1 458640gm1 \([0, 0, 0, -957243, -2214635542]\) \(-662989657192009/14097531093750\) \(-2062655111986560000000\) \([]\) \(25804800\) \(2.7707\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 458640gm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 458640gm do not have complex multiplication.

Modular form 458640.2.a.gm

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