Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 223146em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223146.ba2 | 223146em1 | \([1, -1, 0, 1608, -37178]\) | \(144703125/267674\) | \(-850272617502\) | \([]\) | \(326592\) | \(0.97377\) | \(\Gamma_0(N)\)-optimal |
| 223146.ba1 | 223146em2 | \([1, -1, 0, -15297, 1361429]\) | \(-170953875/244904\) | \(-567120584629368\) | \([]\) | \(979776\) | \(1.5231\) |
Rank
sage: E.rank()
The elliptic curves in class 223146em have rank \(1\).
Complex multiplication
The elliptic curves in class 223146em do not have complex multiplication.Modular form 223146.2.a.em
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
