Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 40656.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.u1 40656s1 \([0, -1, 0, -6816, 614187]\) \(-1235663104/4991679\) \(-141489021454704\) \([]\) \(115200\) \(1.4006\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40656.u1 has rank \(1\).

Complex multiplication

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

Modular form 40656.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 5 q^{13} + q^{15} + 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display