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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 103488.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.fv1 | 103488it4 | \([0, 1, 0, -710369, -230590305]\) | \(1285429208617/614922\) | \(18964796769042432\) | \([2]\) | \(1179648\) | \(2.0783\) | |
| 103488.fv2 | 103488it3 | \([0, 1, 0, -396769, 94462367]\) | \(223980311017/4278582\) | \(131955659562811392\) | \([2]\) | \(1179648\) | \(2.0783\) | |
| 103488.fv3 | 103488it2 | \([0, 1, 0, -51809, -2333409]\) | \(498677257/213444\) | \(6582822019006464\) | \([2, 2]\) | \(589824\) | \(1.7318\) | |
| 103488.fv4 | 103488it1 | \([0, 1, 0, 10911, -263649]\) | \(4657463/3696\) | \(-113988260069376\) | \([2]\) | \(294912\) | \(1.3852\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 103488.fv have rank \(1\).
Complex multiplication
The elliptic curves in class 103488.fv do not have complex multiplication.Modular form 103488.2.a.fv
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.
