Properties

Label 5586.v
Number of curves $1$
Conductor $5586$
CM no
Rank $1$

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

Elliptic curves in class 5586.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.v1 5586t1 \([1, 1, 1, -437865, 111357399]\) \(-3866805342966045361/737311113216\) \(-1770283982831616\) \([]\) \(56448\) \(1.9267\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5586.v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5586.v do not have complex multiplication.

Modular form 5586.2.a.v

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