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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 254898.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254898.et1 | 254898et2 | \([1, -1, 1, -90682619, -334053939733]\) | \(-16591834777/98304\) | \(-488621583046718663786496\) | \([]\) | \(52254720\) | \(3.3858\) | |
| 254898.et2 | 254898et1 | \([1, -1, 1, 2992396, -2444386633]\) | \(596183/864\) | \(-4294525632246550755936\) | \([]\) | \(17418240\) | \(2.8365\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254898.et have rank \(0\).
Complex multiplication
The elliptic curves in class 254898.et do not have complex multiplication.Modular form 254898.2.a.et
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
