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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2496h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.ba4 | 2496h1 | \([0, 1, 0, -92, 18]\) | \(1360251712/771147\) | \(49353408\) | \([2]\) | \(768\) | \(0.16614\) | \(\Gamma_0(N)\)-optimal |
| 2496.ba2 | 2496h2 | \([0, 1, 0, -937, -11305]\) | \(22235451328/123201\) | \(504631296\) | \([2, 2]\) | \(1536\) | \(0.51272\) | |
| 2496.ba1 | 2496h3 | \([0, 1, 0, -14977, -710497]\) | \(11339065490696/351\) | \(11501568\) | \([2]\) | \(3072\) | \(0.85929\) | |
| 2496.ba3 | 2496h4 | \([0, 1, 0, -417, -23265]\) | \(-245314376/6908733\) | \(-226385362944\) | \([2]\) | \(3072\) | \(0.85929\) |
Rank
sage: E.rank()
The elliptic curves in class 2496h have rank \(0\).
Complex multiplication
The elliptic curves in class 2496h do not have complex multiplication.Modular form 2496.2.a.h
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.
