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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 8712.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8712.v1 | 8712s1 | \([0, 0, 0, -91839, -9340958]\) | \(194672/27\) | \(11881340006899968\) | \([2]\) | \(50688\) | \(1.8110\) | \(\Gamma_0(N)\)-optimal |
| 8712.v2 | 8712s2 | \([0, 0, 0, 147741, -49925810]\) | \(202612/729\) | \(-1283184720745196544\) | \([2]\) | \(101376\) | \(2.1576\) |
Rank
sage: E.rank()
The elliptic curves in class 8712.v have rank \(1\).
Complex multiplication
The elliptic curves in class 8712.v do not have complex multiplication.Modular form 8712.2.a.v
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.
