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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 138600y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.cu4 | 138600y1 | \([0, 0, 0, 6225, 7483250]\) | \(9148592/8301447\) | \(-24207019452000000\) | \([2]\) | \(1048576\) | \(1.8228\) | \(\Gamma_0(N)\)-optimal |
| 138600.cu3 | 138600y2 | \([0, 0, 0, -538275, 148508750]\) | \(1478729816932/38900169\) | \(453731571216000000\) | \([2, 2]\) | \(2097152\) | \(2.1694\) | |
| 138600.cu1 | 138600y3 | \([0, 0, 0, -8557275, 9634985750]\) | \(2970658109581346/2139291\) | \(49905380448000000\) | \([2]\) | \(4194304\) | \(2.5159\) | |
| 138600.cu2 | 138600y4 | \([0, 0, 0, -1231275, -312336250]\) | \(8849350367426/3314597517\) | \(77322930876576000000\) | \([2]\) | \(4194304\) | \(2.5159\) |
Rank
sage: E.rank()
The elliptic curves in class 138600y have rank \(0\).
Complex multiplication
The elliptic curves in class 138600y do not have complex multiplication.Modular form 138600.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
