Properties

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

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Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 15680.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dk1 15680bt1 \([0, -1, 0, -65, -223]\) \(-19208/5\) \(-8028160\) \([]\) \(2688\) \(0.041889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 15680.dk1 has rank \(1\).

Complex multiplication

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

Modular form 15680.2.a.dk

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