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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 258570dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 258570.dg2 | 258570dg1 | \([1, -1, 1, 606847, 56334737]\) | \(7023836099951/4456448000\) | \(-15681098596220928000\) | \([]\) | \(5896800\) | \(2.3722\) | \(\Gamma_0(N)\)-optimal |
| 258570.dg1 | 258570dg2 | \([1, -1, 1, -10100993, 12757390481]\) | \(-32391289681150609/1228250000000\) | \(-4321897024448250000000\) | \([]\) | \(17690400\) | \(2.9216\) |
Rank
sage: E.rank()
The elliptic curves in class 258570dg have rank \(0\).
Complex multiplication
The elliptic curves in class 258570dg do not have complex multiplication.Modular form 258570.2.a.dg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
