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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 9702.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.v1 | 9702w3 | \([1, -1, 0, -2277186, -1322083540]\) | \(15226621995131793/2324168\) | \(199334873912328\) | \([2]\) | \(147456\) | \(2.1494\) | |
| 9702.v2 | 9702w4 | \([1, -1, 0, -266226, 20369852]\) | \(24331017010833/12004097336\) | \(1029544864615153656\) | \([2]\) | \(147456\) | \(2.1494\) | |
| 9702.v3 | 9702w2 | \([1, -1, 0, -142746, -20502028]\) | \(3750606459153/45914176\) | \(3937880774431296\) | \([2, 2]\) | \(73728\) | \(1.8029\) | |
| 9702.v4 | 9702w1 | \([1, -1, 0, -1626, -829900]\) | \(-5545233/3469312\) | \(-297549432778752\) | \([2]\) | \(36864\) | \(1.4563\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.v have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.v do not have complex multiplication.Modular form 9702.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
