Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 257754.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257754.e1 257754e1 \([1, 1, 0, -884096, 319610256]\) \(-4499807642857/279888\) \(-4753495492419408\) \([]\) \(4727808\) \(2.0675\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257754.e1 has rank \(2\).

Complex multiplication

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

Modular form 257754.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} - 6 q^{11} - q^{12} + 4 q^{13} - q^{14} + 2 q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display