Properties

Label 12696.e
Number of curves $1$
Conductor $12696$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.e1 12696f1 \([0, -1, 0, -9169, -334955]\) \(-1190106112/243\) \(-17408348928\) \([]\) \(21120\) \(0.96245\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 12696.e do not have complex multiplication.

Modular form 12696.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} - q^{7} + q^{9} + 6q^{11} - 7q^{13} + 2q^{15} + 2q^{17} + O(q^{20})\)  Toggle raw display