Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 36414.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.z1 36414bf1 \([1, -1, 0, -1737, 23949]\) \(2751936625/458752\) \(96650330112\) \([]\) \(34560\) \(0.82908\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36414.z1 has rank \(1\).

Complex multiplication

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

Modular form 36414.2.a.z

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