Properties

Label 287490.e
Number of curves $1$
Conductor $287490$
CM no
Rank $1$

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

Elliptic curves in class 287490.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
287490.e1 287490e1 \([1, 1, 0, -362813, 89281917]\) \(-2058561081361/155400000\) \(-398713883958600000\) \([]\) \(6566400\) \(2.1256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 287490.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 287490.e do not have complex multiplication.

Modular form 287490.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{15} + q^{16} + 7 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display