Properties

Label 257600.el
Number of curves $1$
Conductor $257600$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("el1")
 
E.isogeny_class()
 

Elliptic curves in class 257600.el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.el1 257600el1 \([0, 1, 0, -2833, 57463]\) \(-157216000/1127\) \(-18032000000\) \([]\) \(221184\) \(0.80038\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.el1 has rank \(1\).

Complex multiplication

The elliptic curves in class 257600.el do not have complex multiplication.

Modular form 257600.2.a.el

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} - 2 q^{9} + 6 q^{11} - 3 q^{13} + O(q^{20})\) Copy content Toggle raw display