Properties

Label 66759e
Number of curves $1$
Conductor $66759$
CM no
Rank $1$

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

Elliptic curves in class 66759e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66759.h1 66759e1 \([1, 0, 1, 7363, -1285063]\) \(1829276567/30642381\) \(-739632585711789\) \([]\) \(276480\) \(1.5336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66759e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66759e do not have complex multiplication.

Modular form 66759.2.a.e

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