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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 236691.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236691.u1 | 236691u3 | \([1, -1, 0, -64380006, 198842763087]\) | \(1677087406638588673/4641\) | \(81664371684441\) | \([2]\) | \(11796480\) | \(2.7879\) | |
| 236691.u2 | 236691u2 | \([1, -1, 0, -4023801, 3107590272]\) | \(409460675852593/21538881\) | \(379004348987490681\) | \([2, 2]\) | \(5898240\) | \(2.4413\) | |
| 236691.u3 | 236691u4 | \([1, -1, 0, -3802716, 3464023509]\) | \(-345608484635233/94427721297\) | \(-1661577360334628997897\) | \([2]\) | \(11796480\) | \(2.7879\) | |
| 236691.u4 | 236691u1 | \([1, -1, 0, -265356, 42954219]\) | \(117433042273/22801233\) | \(401217058085658633\) | \([2]\) | \(2949120\) | \(2.0947\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236691.u have rank \(0\).
Complex multiplication
The elliptic curves in class 236691.u do not have complex multiplication.Modular form 236691.2.a.u
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.
