Properties

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

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 40656.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40656.by1 40656do1 \([0, 1, 0, 48, -684]\) \(24167/441\) \(-218566656\) \([]\) \(18432\) \(0.28066\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40656.by1 has rank \(1\).

Complex multiplication

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

Modular form 40656.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} + q^{7} + q^{9} - 7 q^{13} - 3 q^{15} - 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display