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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 89232.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89232.c1 | 89232bf2 | \([0, -1, 0, -7778112, 8190483456]\) | \(92162208697/2044416\) | \(1154417076109169393664\) | \([]\) | \(7278336\) | \(2.8291\) | |
| 89232.c2 | 89232bf1 | \([0, -1, 0, -923472, -336688704]\) | \(154241737/2376\) | \(1341652077089685504\) | \([]\) | \(2426112\) | \(2.2798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89232.c have rank \(0\).
Complex multiplication
The elliptic curves in class 89232.c do not have complex multiplication.Modular form 89232.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
