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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 705600.et
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.et1 | \([0, 0, 0, -49406700, -133667786000]\) | \(303735479048/105\) | \(4610786664960000000\) | \([2]\) | \(56623104\) | \(2.9371\) |
| 705600.et2 | \([0, 0, 0, -3101700, -2068976000]\) | \(601211584/11025\) | \(60516574977600000000\) | \([2, 2]\) | \(28311552\) | \(2.5906\) |
| 705600.et3 | \([0, 0, 0, -400575, 48706000]\) | \(82881856/36015\) | \(3088866847815000000\) | \([2]\) | \(14155776\) | \(2.2440\) |
| 705600.et4 | \([0, 0, 0, -14700, -6001814000]\) | \(-8/354375\) | \(-15561404994240000000000\) | \([2]\) | \(56623104\) | \(2.9371\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.et have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.et do not have complex multiplication.Modular form 705600.2.a.et
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
