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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 259920bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.bz4 | 259920bz1 | \([0, 0, 0, 63897, -10850938]\) | \(3286064/7695\) | \(-67561257364750080\) | \([2]\) | \(2211840\) | \(1.9133\) | \(\Gamma_0(N)\)-optimal |
| 259920.bz3 | 259920bz2 | \([0, 0, 0, -520923, -119744422]\) | \(445138564/81225\) | \(2852586422067225600\) | \([2, 2]\) | \(4423680\) | \(2.2599\) | |
| 259920.bz2 | 259920bz3 | \([0, 0, 0, -2470323, 1384022738]\) | \(23735908082/1954815\) | \(137304493115502458880\) | \([2]\) | \(8847360\) | \(2.6065\) | |
| 259920.bz1 | 259920bz4 | \([0, 0, 0, -7928643, -8592694558]\) | \(784767874322/35625\) | \(2502268791287040000\) | \([2]\) | \(8847360\) | \(2.6065\) |
Rank
sage: E.rank()
The elliptic curves in class 259920bz have rank \(1\).
Complex multiplication
The elliptic curves in class 259920bz do not have complex multiplication.Modular form 259920.2.a.bz
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.
