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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 222024f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222024.t3 | 222024f1 | \([0, 1, 0, -10372, -395488]\) | \(810448/33\) | \(5025067415808\) | \([2]\) | \(401408\) | \(1.2029\) | \(\Gamma_0(N)\)-optimal |
| 222024.t2 | 222024f2 | \([0, 1, 0, -27192, 1192320]\) | \(3650692/1089\) | \(663308898886656\) | \([2, 2]\) | \(802816\) | \(1.5495\) | |
| 222024.t1 | 222024f3 | \([0, 1, 0, -397232, 96218592]\) | \(5690357426/891\) | \(1085414561814528\) | \([2]\) | \(1605632\) | \(1.8961\) | |
| 222024.t4 | 222024f4 | \([0, 1, 0, 73728, 8054880]\) | \(36382894/43923\) | \(-53506917843523584\) | \([2]\) | \(1605632\) | \(1.8961\) |
Rank
sage: E.rank()
The elliptic curves in class 222024f have rank \(1\).
Complex multiplication
The elliptic curves in class 222024f do not have complex multiplication.Modular form 222024.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
