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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 170093.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170093.c1 | 170093c1 | \([0, 1, 1, -197337, -33807293]\) | \(-78843215872/539\) | \(-5809997062331\) | \([]\) | \(706560\) | \(1.6301\) | \(\Gamma_0(N)\)-optimal |
| 170093.c2 | 170093c2 | \([0, 1, 1, -108977, -64059548]\) | \(-13278380032/156590819\) | \(-1687926156545464451\) | \([]\) | \(2119680\) | \(2.1794\) | |
| 170093.c3 | 170093c3 | \([0, 1, 1, 973433, 1657513557]\) | \(9463555063808/115539436859\) | \(-1245424468894560411611\) | \([]\) | \(6359040\) | \(2.7287\) |
Rank
sage: E.rank()
The elliptic curves in class 170093.c have rank \(2\).
Complex multiplication
The elliptic curves in class 170093.c do not have complex multiplication.Modular form 170093.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
