Properties

Label 2142a
Number of curves $1$
Conductor $2142$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 2142a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2142.e1 2142a1 \([1, -1, 0, -474, -5068]\) \(-599077107/243712\) \(-4796983296\) \([]\) \(1056\) \(0.56608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2142a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2142a do not have complex multiplication.

Modular form 2142.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{11} - 3 q^{13} + q^{14} + q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display