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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5712v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5712.y1 | 5712v1 | \([0, 1, 0, -337, 2270]\) | \(265327034368/297381\) | \(4758096\) | \([2]\) | \(1440\) | \(0.19534\) | \(\Gamma_0(N)\)-optimal |
| 5712.y2 | 5712v2 | \([0, 1, 0, -252, 3528]\) | \(-6940769488/18000297\) | \(-4608076032\) | \([2]\) | \(2880\) | \(0.54191\) |
Rank
sage: E.rank()
The elliptic curves in class 5712v have rank \(0\).
Complex multiplication
The elliptic curves in class 5712v do not have complex multiplication.Modular form 5712.2.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 Cremona 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 Cremona labels.
