Properties

Label 36414.cz
Number of curves $1$
Conductor $36414$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 36414.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.cz1 36414cx1 \([1, -1, 1, 169699, -88979547]\) \(150900148890919/1041386274432\) \(-3729805128621339264\) \([]\) \(680960\) \(2.2452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36414.cz1 has rank \(0\).

Complex multiplication

The elliptic curves in class 36414.cz do not have complex multiplication.

Modular form 36414.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} + q^{11} + q^{13} + q^{14} + q^{16} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display