Properties

Label 38720cz
Number of curves $1$
Conductor $38720$
CM no
Rank $1$

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

Elliptic curves in class 38720cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38720.e1 38720cz1 \([0, 0, 0, 308, 1936]\) \(9261/10\) \(-3489136640\) \([]\) \(46080\) \(0.51769\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38720cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 38720cz do not have complex multiplication.

Modular form 38720.2.a.cz

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} - 4 q^{13} - 3 q^{15} - q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display