Properties

Label 2142.f
Number of curves $1$
Conductor $2142$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2142.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2142.f1 2142c1 \([1, -1, 0, 156, -144]\) \(15494117157/9143008\) \(-246861216\) \([]\) \(800\) \(0.29973\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2142.f1 has rank \(1\).

Complex multiplication

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

Modular form 2142.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 3 q^{11} - 5 q^{13} - q^{14} + q^{16} + q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display