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SageMath
E = EllipticCurve("iy1")
E.isogeny_class()
Elliptic curves in class 705600.iy
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.iy1 | \([0, 0, 0, -983268300, 7348530098000]\) | \(2394165105226952/854262178245\) | \(37512577712683129674240000000\) | \([2]\) | \(566231040\) | \(4.1838\) |
| 705600.iy2 | \([0, 0, 0, -875223300, 9963867368000]\) | \(13507798771700416/3544416225\) | \(19455413172973646400000000\) | \([2, 2]\) | \(283115520\) | \(3.8372\) |
| 705600.iy3 | \([0, 0, 0, -875168175, 9965185517000]\) | \(864335783029582144/59535\) | \(5106086013735000000\) | \([2]\) | \(141557760\) | \(3.4907\) |
| 705600.iy4 | \([0, 0, 0, -768060300, 12494843102000]\) | \(-1141100604753992/875529151875\) | \(-38446458459514176960000000000\) | \([2]\) | \(566231040\) | \(4.1838\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.iy have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.iy do not have complex multiplication.Modular form 705600.2.a.iy
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.
