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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 24843s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24843.h4 | 24843s1 | \([1, 0, 0, 3968, 205295]\) | \(12167/39\) | \(-22146900829599\) | \([2]\) | \(48384\) | \(1.2439\) | \(\Gamma_0(N)\)-optimal |
| 24843.h3 | 24843s2 | \([1, 0, 0, -37437, 2399760]\) | \(10218313/1521\) | \(863729132354361\) | \([2, 2]\) | \(96768\) | \(1.5905\) | |
| 24843.h2 | 24843s3 | \([1, 0, 0, -161652, -22666827]\) | \(822656953/85683\) | \(48656741122629003\) | \([2]\) | \(193536\) | \(1.9371\) | |
| 24843.h1 | 24843s4 | \([1, 0, 0, -575702, 168077727]\) | \(37159393753/1053\) | \(597966322399173\) | \([2]\) | \(193536\) | \(1.9371\) |
Rank
sage: E.rank()
The elliptic curves in class 24843s have rank \(1\).
Complex multiplication
The elliptic curves in class 24843s do not have complex multiplication.Modular form 24843.2.a.s
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.
