Properties

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

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Show commands: SageMath
E = EllipticCurve("gg1")
 
E.isogeny_class()
 

Elliptic curves in class 257600.gg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.gg1 257600gg1 \([0, 0, 0, -841900, 301667000]\) \(-4124632486295808/70140333767\) \(-1122245340272000000\) \([]\) \(5505024\) \(2.2620\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.gg1 has rank \(1\).

Complex multiplication

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

Modular form 257600.2.a.gg

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + q^{7} + 6 q^{9} - 2 q^{11} - q^{13} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display