Properties

Label 86640.v
Number of curves $1$
Conductor $86640$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 86640.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.v1 86640cd1 \([0, -1, 0, -677842961, 6793400894640]\) \(-351119534556135424/29056536675\) \(-2850360825226396181626800\) \([]\) \(21833280\) \(3.7367\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 86640.v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 86640.v do not have complex multiplication.

Modular form 86640.2.a.v

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