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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 177600iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177600.cv2 | 177600iz1 | \([0, -1, 0, -1833633, -1508464863]\) | \(-166456688365729/143856000000\) | \(-589234176000000000000\) | \([2]\) | \(5529600\) | \(2.6829\) | \(\Gamma_0(N)\)-optimal |
| 177600.cv1 | 177600iz2 | \([0, -1, 0, -33833633, -75716464863]\) | \(1045706191321645729/323352324000\) | \(1324451119104000000000\) | \([2]\) | \(11059200\) | \(3.0294\) |
Rank
sage: E.rank()
The elliptic curves in class 177600iz have rank \(1\).
Complex multiplication
The elliptic curves in class 177600iz do not have complex multiplication.Modular form 177600.2.a.iz
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
