Properties

Label 363726.z
Number of curves $1$
Conductor $363726$
CM no
Rank $1$

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

Elliptic curves in class 363726.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363726.z1 363726z1 \([1, -1, 0, 53091, -5136939]\) \(187615592384231/237141728784\) \(-20918034754307856\) \([]\) \(2617344\) \(1.8176\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 363726.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 363726.z do not have complex multiplication.

Modular form 363726.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - 4 q^{7} - q^{8} - q^{10} + q^{13} + 4 q^{14} + q^{16} - 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display