Properties

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

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Show commands: SageMath
E = EllipticCurve("es1")
 
E.isogeny_class()
 

Elliptic curves in class 257600.es

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.es1 257600es1 \([0, 1, 0, -1373, 19133]\) \(-35806478336/3703\) \(-29624000\) \([]\) \(78336\) \(0.46619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.es1 has rank \(1\).

Complex multiplication

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

Modular form 257600.2.a.es

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2 q^{9} + q^{11} + q^{13} - q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display