Properties

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

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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 458640fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.fb1 458640fb1 \([0, 0, 0, 42, -497]\) \(14336/195\) \(-111449520\) \([]\) \(138240\) \(0.22484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 458640fb1 has rank \(1\).

Complex multiplication

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

Modular form 458640.2.a.fb

sage: E.q_eigenform(10)
 
\(q - q^{5} + 3 q^{11} - q^{13} - 3 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display