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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 319073.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 319073.a1 | 319073a4 | \([1, -1, 1, -1702114, -854308280]\) | \(82483294977/17\) | \(112401556260353\) | \([2]\) | \(2585088\) | \(2.0834\) | |
| 319073.a2 | 319073a2 | \([1, -1, 1, -106749, -13231852]\) | \(20346417/289\) | \(1910826456426001\) | \([2, 2]\) | \(1292544\) | \(1.7368\) | |
| 319073.a3 | 319073a3 | \([1, -1, 1, -12904, -35754652]\) | \(-35937/83521\) | \(-552228845907114289\) | \([2]\) | \(2585088\) | \(2.0834\) | |
| 319073.a4 | 319073a1 | \([1, -1, 1, -12904, 244290]\) | \(35937/17\) | \(112401556260353\) | \([2]\) | \(646272\) | \(1.3902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 319073.a have rank \(0\).
Complex multiplication
The elliptic curves in class 319073.a do not have complex multiplication.Modular form 319073.2.a.a
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 LMFDB 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 LMFDB labels.
