Properties

Label 458640.f
Number of curves $1$
Conductor $458640$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 458640.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.f1 458640f1 \([0, 0, 0, -37443, 3016258]\) \(-39678209809/3900000\) \(-570621542400000\) \([]\) \(1843200\) \(1.5722\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 458640.f1 has rank \(1\).

Complex multiplication

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

Modular form 458640.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6 q^{11} + q^{13} - q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display