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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 37440.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.dc1 | 37440s4 | \([0, 0, 0, -2303532, -1345672656]\) | \(261984288445803/42250\) | \(218000719872000\) | \([2]\) | \(663552\) | \(2.1535\) | |
| 37440.dc2 | 37440s3 | \([0, 0, 0, -143532, -21160656]\) | \(-63378025803/812500\) | \(-4192321536000000\) | \([2]\) | \(331776\) | \(1.8070\) | |
| 37440.dc3 | 37440s2 | \([0, 0, 0, -32172, -1330384]\) | \(520300455507/193072360\) | \(1366544539975680\) | \([2]\) | \(221184\) | \(1.6042\) | |
| 37440.dc4 | 37440s1 | \([0, 0, 0, 6228, -147664]\) | \(3774555693/3515200\) | \(-24880191897600\) | \([2]\) | \(110592\) | \(1.2576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 37440.dc do not have complex multiplication.Modular form 37440.2.a.dc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
