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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 15600bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.p3 | 15600bf1 | \([0, -1, 0, -5408, -146688]\) | \(273359449/9360\) | \(599040000000\) | \([2]\) | \(18432\) | \(1.0318\) | \(\Gamma_0(N)\)-optimal |
| 15600.p2 | 15600bf2 | \([0, -1, 0, -13408, 397312]\) | \(4165509529/1368900\) | \(87609600000000\) | \([2, 2]\) | \(36864\) | \(1.3783\) | |
| 15600.p1 | 15600bf3 | \([0, -1, 0, -193408, 32797312]\) | \(12501706118329/2570490\) | \(164511360000000\) | \([4]\) | \(73728\) | \(1.7249\) | |
| 15600.p4 | 15600bf4 | \([0, -1, 0, 38592, 2685312]\) | \(99317171591/106616250\) | \(-6823440000000000\) | \([2]\) | \(73728\) | \(1.7249\) |
Rank
sage: E.rank()
The elliptic curves in class 15600bf have rank \(1\).
Complex multiplication
The elliptic curves in class 15600bf do not have complex multiplication.Modular form 15600.2.a.bf
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.
