Properties

Label 361998.z
Number of curves $1$
Conductor $361998$
CM no
Rank $1$

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

Elliptic curves in class 361998.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361998.z1 361998z1 \([1, -1, 0, 1748936268, 11045149068240]\) \(76529339407951422875/51105601752662016\) \(-395081055550568304269875740672\) \([]\) \(378892800\) \(4.3678\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 361998.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 361998.z do not have complex multiplication.

Modular form 361998.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 4 q^{11} + q^{14} + q^{16} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display