Properties

Label 31920.cf
Number of curves $1$
Conductor $31920$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 31920.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31920.cf1 31920by1 \([0, 1, 0, 19000, 784500]\) \(185183253170999/171032148000\) \(-700547678208000\) \([]\) \(138240\) \(1.5358\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31920.cf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 31920.cf do not have complex multiplication.

Modular form 31920.2.a.cf

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