Properties

Label 122304cz
Number of curves $1$
Conductor $122304$
CM no
Rank $1$

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

Elliptic curves in class 122304cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122304.gz1 122304cz1 \([0, 1, 0, -23585, 1594431]\) \(-47045881/8736\) \(-269426796527616\) \([]\) \(368640\) \(1.4934\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122304cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 122304cz do not have complex multiplication.

Modular form 122304.2.a.cz

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