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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 353600dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 353600.dg1 | 353600dg1 | \([0, 0, 0, -28300, -822000]\) | \(611960049/282880\) | \(1158676480000000\) | \([2]\) | \(1179648\) | \(1.5852\) | \(\Gamma_0(N)\)-optimal |
| 353600.dg2 | 353600dg2 | \([0, 0, 0, 99700, -6198000]\) | \(26757728271/19536400\) | \(-80021094400000000\) | \([2]\) | \(2359296\) | \(1.9317\) |
Rank
sage: E.rank()
The elliptic curves in class 353600dg have rank \(0\).
Complex multiplication
The elliptic curves in class 353600dg do not have complex multiplication.Modular form 353600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
