Properties

Label 2160.e
Number of curves $1$
Conductor $2160$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2160.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2160.e1 2160c1 \([0, 0, 0, -3, -3]\) \(-6912/5\) \(-2160\) \([]\) \(96\) \(-0.66052\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2160.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2160.e do not have complex multiplication.

Modular form 2160.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} + 4 q^{11} - 2 q^{13} - 5 q^{17} + 5 q^{19} + O(q^{20})\)  Toggle raw display