Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 257600.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.a1 257600a1 \([0, 0, 0, -1300, -49250]\) \(-242970624/907235\) \(-907235000000\) \([]\) \(691200\) \(0.98014\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.a1 has rank \(1\).

Complex multiplication

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

Modular form 257600.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - q^{7} + 6 q^{9} - q^{11} + 7 q^{13} - 3 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display