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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 70560dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.e3 | 70560dm1 | \([0, 0, 0, -2793, 19208]\) | \(438976/225\) | \(1235032142400\) | \([2, 2]\) | \(98304\) | \(1.0124\) | \(\Gamma_0(N)\)-optimal |
| 70560.e4 | 70560dm2 | \([0, 0, 0, 10437, 148862]\) | \(2863288/1875\) | \(-82335476160000\) | \([2]\) | \(196608\) | \(1.3590\) | |
| 70560.e2 | 70560dm3 | \([0, 0, 0, -24843, -1493422]\) | \(38614472/405\) | \(17784462850560\) | \([2]\) | \(196608\) | \(1.3590\) | |
| 70560.e1 | 70560dm4 | \([0, 0, 0, -35868, 2612288]\) | \(14526784/15\) | \(5269470474240\) | \([2]\) | \(196608\) | \(1.3590\) |
Rank
sage: E.rank()
The elliptic curves in class 70560dm have rank \(2\).
Complex multiplication
The elliptic curves in class 70560dm do not have complex multiplication.Modular form 70560.2.a.dm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
