Properties

Label 40656bg
Number of curves $1$
Conductor $40656$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 40656bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.p1 40656bg1 \([0, -1, 0, -206466, -36041553]\) \(-34339609640704/916839\) \(-25987779450864\) \([]\) \(172800\) \(1.6790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40656bg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40656bg do not have complex multiplication.

Modular form 40656.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - q^{13} + q^{15} - 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display