Properties

Label 230640.z
Number of curves $1$
Conductor $230640$
CM no
Rank $1$

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

Elliptic curves in class 230640.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230640.z1 230640z1 \([0, -1, 0, -230960, 46483392]\) \(-360187951921/37500000\) \(-141852825600000000\) \([]\) \(3456000\) \(2.0303\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 230640.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 230640.z do not have complex multiplication.

Modular form 230640.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 5 q^{7} + q^{9} + q^{11} + 4 q^{13} - q^{15} + 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display