Properties

Label 12696.b
Number of curves $1$
Conductor $12696$
CM no
Rank $2$

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.b1 12696h1 \([0, -1, 0, 8, 316]\) \(92/81\) \(-43877376\) \([]\) \(3840\) \(0.14543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.b1 has rank \(2\).

Complex multiplication

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

Modular form 12696.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3q^{5} - 4q^{7} + q^{9} - q^{13} + 3q^{15} - 2q^{17} + O(q^{20})\)  Toggle raw display