Properties

Label 15680.w
Number of curves $1$
Conductor $15680$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 15680.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.w1 15680bw1 \([0, 1, 0, -65, 223]\) \(-19208/5\) \(-8028160\) \([]\) \(2688\) \(0.041889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 15680.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 15680.w do not have complex multiplication.

Modular form 15680.2.a.w

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