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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 33600en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.ch3 | 33600en1 | \([0, -1, 0, -908, 5562]\) | \(82881856/36015\) | \(36015000000\) | \([2]\) | \(36864\) | \(0.72173\) | \(\Gamma_0(N)\)-optimal |
| 33600.ch2 | 33600en2 | \([0, -1, 0, -7033, -221063]\) | \(601211584/11025\) | \(705600000000\) | \([2, 2]\) | \(73728\) | \(1.0683\) | |
| 33600.ch4 | 33600en3 | \([0, -1, 0, -33, -648063]\) | \(-8/354375\) | \(-181440000000000\) | \([2]\) | \(147456\) | \(1.4149\) | |
| 33600.ch1 | 33600en4 | \([0, -1, 0, -112033, -14396063]\) | \(303735479048/105\) | \(53760000000\) | \([2]\) | \(147456\) | \(1.4149\) |
Rank
sage: E.rank()
The elliptic curves in class 33600en have rank \(0\).
Complex multiplication
The elliptic curves in class 33600en do not have complex multiplication.Modular form 33600.2.a.en
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
