Properties

Label 40656.s
Number of curves $1$
Conductor $40656$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 40656.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.s1 40656r1 \([0, -1, 0, -161, 717]\) \(123904/21\) \(78710016\) \([]\) \(10752\) \(0.23585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40656.s1 has rank \(1\).

Complex multiplication

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

Modular form 40656.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} + 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display