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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 705600.hu
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.hu1 | \([0, 0, 0, -14289120300, -657440340298000]\) | \(7347751505995469192/72930375\) | \(3202537147814592000000000\) | \([2]\) | \(566231040\) | \(4.2784\) |
| 705600.hu2 | \([0, 0, 0, -1279620300, -537544798000]\) | \(5276930158229192/3050936350875\) | \(133973491831011177408000000000\) | \([2]\) | \(566231040\) | \(4.2784\) |
| 705600.hu3 | \([0, 0, 0, -893745300, -10256192548000]\) | \(14383655824793536/45209390625\) | \(248155780267521000000000000\) | \([2, 2]\) | \(283115520\) | \(3.9319\) |
| 705600.hu4 | \([0, 0, 0, -32417175, -295794110500]\) | \(-43927191786304/415283203125\) | \(-35617229448486328125000000\) | \([2]\) | \(141557760\) | \(3.5853\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.hu have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.hu do not have complex multiplication.Modular form 705600.2.a.hu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
