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)
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.