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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 16224j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16224.u1 | 16224j1 | \([0, 1, 0, -2422, 35972]\) | \(5088448/1053\) | \(325288312128\) | \([2]\) | \(21504\) | \(0.92418\) | \(\Gamma_0(N)\)-optimal |
| 16224.u2 | 16224j2 | \([0, 1, 0, 5183, 223055]\) | \(778688/1521\) | \(-30071097298944\) | \([2]\) | \(43008\) | \(1.2708\) |
Rank
sage: E.rank()
The elliptic curves in class 16224j have rank \(0\).
Complex multiplication
The elliptic curves in class 16224j do not have complex multiplication.Modular form 16224.2.a.j
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.
