Properties

Label 257754.i
Number of curves $1$
Conductor $257754$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 257754.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.i1 257754i1 \([1, 1, 0, -346605, -78686307]\) \(-12756247537586784625/329148288\) \(-118822531968\) \([]\) \(1451520\) \(1.6410\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754.i1 has rank \(2\).

Complex multiplication

The elliptic curves in class 257754.i do not have complex multiplication.

Modular form 257754.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - 5 q^{11} - q^{12} - q^{13} + q^{14} + q^{16} - q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display