Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.m1 12696b1 \([0, -1, 0, -196872, -33556500]\) \(-778918741604594/27\) \(-29251584\) \([]\) \(31680\) \(1.3796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.m1 has rank \(0\).

Complex multiplication

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

Modular form 12696.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} + q^{7} + q^{9} + 5q^{11} + 4q^{13} - 2q^{15} - 2q^{17} + O(q^{20})\)  Toggle raw display