Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 2142o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2142.o1 2142o1 \([1, -1, 1, -338, 2553]\) \(-5841725401/231336\) \(-168643944\) \([]\) \(960\) \(0.34722\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2142o1 has rank \(1\).

Complex multiplication

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

Modular form 2142.2.a.o

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