Properties

Label 13860.a
Number of curves $1$
Conductor $13860$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 13860.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.a1 13860j1 \([0, 0, 0, -17677848, -28621396172]\) \(-3273741656681120014336/1733575611796875\) \(-323526814975980000000\) \([]\) \(725760\) \(2.8854\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13860.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 13860.a do not have complex multiplication.

Modular form 13860.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - q^{11} - 6 q^{13} + 3 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display