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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 92697.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92697.c1 | 92697e4 | \([1, 0, 0, -411577, 101496542]\) | \(347873904937/395307\) | \(8761727104821603\) | \([2]\) | \(898560\) | \(1.9725\) | |
| 92697.c2 | 92697e2 | \([1, 0, 0, -32362, 701195]\) | \(169112377/88209\) | \(1955096130827961\) | \([2, 2]\) | \(449280\) | \(1.6259\) | |
| 92697.c3 | 92697e1 | \([1, 0, 0, -18317, -947688]\) | \(30664297/297\) | \(6582815255313\) | \([2]\) | \(224640\) | \(1.2794\) | \(\Gamma_0(N)\)-optimal |
| 92697.c4 | 92697e3 | \([1, 0, 0, 122133, 5490540]\) | \(9090072503/5845851\) | \(-129569552670325779\) | \([2]\) | \(898560\) | \(1.9725\) |
Rank
sage: E.rank()
The elliptic curves in class 92697.c have rank \(1\).
Complex multiplication
The elliptic curves in class 92697.c do not have complex multiplication.Modular form 92697.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
