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SageMath
E = EllipticCurve("os1")
E.isogeny_class()
Elliptic curves in class 100800.os
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.os1 | 100800nu4 | \([0, 0, 0, -20066700, 21424286000]\) | \(2394165105226952/854262178245\) | \(318851649505589760000000\) | \([2]\) | \(11796480\) | \(3.2109\) | |
100800.os2 | 100800nu2 | \([0, 0, 0, -17861700, 29049176000]\) | \(13507798771700416/3544416225\) | \(165368283393600000000\) | \([2, 2]\) | \(5898240\) | \(2.8643\) | |
100800.os3 | 100800nu1 | \([0, 0, 0, -17860575, 29053019000]\) | \(864335783029582144/59535\) | \(43401015000000\) | \([2]\) | \(2949120\) | \(2.5177\) | \(\Gamma_0(N)\)-optimal |
100800.os4 | 100800nu3 | \([0, 0, 0, -15674700, 36428114000]\) | \(-1141100604753992/875529151875\) | \(-326789504879040000000000\) | \([2]\) | \(11796480\) | \(3.2109\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.os have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.os do not have complex multiplication.Modular form 100800.2.a.os
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.