Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.f1 12696m1 \([0, -1, 0, 31, -75]\) \(23552/27\) \(-3656448\) \([]\) \(1152\) \(-0.054289\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.f1 has rank \(1\).

Complex multiplication

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

Modular form 12696.2.a.f

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