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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 69360.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.be1 | 69360cy4 | \([0, -1, 0, -30245680, 64033278400]\) | \(30949975477232209/478125000\) | \(47271015129600000000\) | \([4]\) | \(5308416\) | \(2.9103\) | |
| 69360.be2 | 69360cy2 | \([0, -1, 0, -1946800, 938095552]\) | \(8253429989329/936360000\) | \(92575556029808640000\) | \([2, 2]\) | \(2654208\) | \(2.5637\) | |
| 69360.be3 | 69360cy1 | \([0, -1, 0, -467120, -107150400]\) | \(114013572049/15667200\) | \(1548976623766732800\) | \([2]\) | \(1327104\) | \(2.2171\) | \(\Gamma_0(N)\)-optimal |
| 69360.be4 | 69360cy3 | \([0, -1, 0, 2677200, 4714978752]\) | \(21464092074671/109596256200\) | \(-10835505955508952268800\) | \([2]\) | \(5308416\) | \(2.9103\) |
Rank
sage: E.rank()
The elliptic curves in class 69360.be have rank \(1\).
Complex multiplication
The elliptic curves in class 69360.be do not have complex multiplication.Modular form 69360.2.a.be
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.
