Properties

Label 66759.i
Number of curves $1$
Conductor $66759$
CM no
Rank $1$

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

Elliptic curves in class 66759.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66759.i1 66759c1 \([0, -1, 1, 1638, -2519323]\) \(69632/392931\) \(-2740991347049571\) \([]\) \(587520\) \(1.6412\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66759.i1 has rank \(1\).

Complex multiplication

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

Modular form 66759.2.a.i

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