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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7098.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7098.k1 | 7098o3 | \([1, 0, 1, -2284377, 1328255164]\) | \(124318741396429/51631104\) | \(547522009995297792\) | \([2]\) | \(156000\) | \(2.3655\) | |
| 7098.k2 | 7098o4 | \([1, 0, 1, -1932857, 1751063420]\) | \(-75306487574989/81352871712\) | \(-862706477061653436576\) | \([2]\) | \(312000\) | \(2.7121\) | |
| 7098.k3 | 7098o1 | \([1, 0, 1, -76392, -8122814]\) | \(4649101309/6804\) | \(72153013733892\) | \([2]\) | \(31200\) | \(1.5608\) | \(\Gamma_0(N)\)-optimal |
| 7098.k4 | 7098o2 | \([1, 0, 1, -54422, -12885910]\) | \(-1680914269/5786802\) | \(-61366138180675146\) | \([2]\) | \(62400\) | \(1.9074\) |
Rank
sage: E.rank()
The elliptic curves in class 7098.k have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.k do not have complex multiplication.Modular form 7098.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
