Properties

Label 15680cm
Number of curves $1$
Conductor $15680$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 15680cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.z1 15680cm1 \([0, -1, 0, -23781, 1422205]\) \(-2249728/5\) \(-3305767485440\) \([]\) \(43008\) \(1.2850\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 15680cm1 has rank \(1\).

Complex multiplication

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

Modular form 15680.2.a.cm

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{9} - 5 q^{11} + 7 q^{13} + q^{15} + 3 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display