Properties

Label 62866.f
Number of curves $1$
Conductor $62866$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 62866.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62866.f1 62866f1 \([1, 0, 0, 10131, -129919]\) \(18191447/11696\) \(-73934662221104\) \([]\) \(177408\) \(1.3501\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 62866.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 62866.f do not have complex multiplication.

Modular form 62866.2.a.f

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