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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 436800.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 436800.r1 | 436800r1 | \([0, -1, 0, -3368, -74118]\) | \(528297936704/24843\) | \(198744000\) | \([2]\) | \(270336\) | \(0.66656\) | \(\Gamma_0(N)\)-optimal |
| 436800.r2 | 436800r2 | \([0, -1, 0, -3193, -82343]\) | \(-7033743296/1799343\) | \(-921263616000\) | \([2]\) | \(540672\) | \(1.0131\) |
Rank
sage: E.rank()
The elliptic curves in class 436800.r have rank \(0\).
Complex multiplication
The elliptic curves in class 436800.r do not have complex multiplication.Modular form 436800.2.a.r
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.
