Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.d1 12696e1 \([0, -1, 0, -104145464, 409115098764]\) \(-778918741604594/27\) \(-4330284242098176\) \([]\) \(728640\) \(2.9473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.d1 has rank \(0\).

Complex multiplication

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

Modular form 12696.2.a.d

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