Properties

Label 2142q
Number of curves $2$
Conductor $2142$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 2142q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2142.n2 2142q1 \([1, -1, 1, -30011, -2242389]\) \(-4100379159705193/626805817344\) \(-456941440843776\) \([2]\) \(10752\) \(1.5421\) \(\Gamma_0(N)\)-optimal
2142.n1 2142q2 \([1, -1, 1, -496571, -134558805]\) \(18575453384550358633/352517816448\) \(256985488190592\) \([2]\) \(21504\) \(1.8887\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2142q have rank \(0\).

Complex multiplication

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

Modular form 2142.2.a.q

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.