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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 200277.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200277.z1 | 200277v1 | \([1, -1, 0, -574867872, -5305036839813]\) | \(1194006714002239614625/3066040593\) | \(53950932683976705993\) | \([2]\) | \(33177600\) | \(3.4492\) | \(\Gamma_0(N)\)-optimal |
| 200277.z2 | 200277v2 | \([1, -1, 0, -574646787, -5309321334462]\) | \(-1192629656009513436625/1913414394041073\) | \(-33668990360122739922850473\) | \([2]\) | \(66355200\) | \(3.7957\) |
Rank
sage: E.rank()
The elliptic curves in class 200277.z have rank \(0\).
Complex multiplication
The elliptic curves in class 200277.z do not have complex multiplication.Modular form 200277.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
