Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.j1 12696k1 \([0, -1, 0, 16223, 782293]\) \(23552/27\) \(-541285530262272\) \([]\) \(26496\) \(1.5135\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12696.j1 has rank \(1\).

Complex multiplication

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

Modular form 12696.2.a.j

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