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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 348726.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348726.c1 | 348726c1 | \([1, 1, 0, -560612209656, -161523012846271680]\) | \(414180609320646251159036261381137/119360941233396540720021504\) | \(5615440637314366880525785994625024\) | \([2]\) | \(7280824320\) | \(5.4559\) | \(\Gamma_0(N)\)-optimal |
| 348726.c2 | 348726c2 | \([1, 1, 0, -488690381816, -204488005201738944]\) | \(-274349062822440138956705327559697/225202879880369216454056214528\) | \(-10594867887709144393360770635994759168\) | \([2]\) | \(14561648640\) | \(5.8025\) |
Rank
sage: E.rank()
The elliptic curves in class 348726.c have rank \(0\).
Complex multiplication
The elliptic curves in class 348726.c do not have complex multiplication.Modular form 348726.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
