Properties

Label 257600en
Number of curves $1$
Conductor $257600$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("en1")
 
E.isogeny_class()
 

Elliptic curves in class 257600en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.en1 257600en1 \([0, 1, 0, -347333, -196275037]\) \(-144814859264/435654247\) \(-13940935904000000000\) \([]\) \(4157440\) \(2.3602\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600en1 has rank \(2\).

Complex multiplication

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

Modular form 257600.2.a.en

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