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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 15600.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.x1 | 15600bv1 | \([0, -1, 0, -40708, -16727588]\) | \(-74605986640/1167575877\) | \(-116757587700000000\) | \([]\) | \(103680\) | \(1.9562\) | \(\Gamma_0(N)\)-optimal |
| 15600.x2 | 15600bv2 | \([0, -1, 0, 364292, 437682412]\) | \(53465227872560/858964449213\) | \(-85896444921300000000\) | \([]\) | \(311040\) | \(2.5055\) |
Rank
sage: E.rank()
The elliptic curves in class 15600.x have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.x do not have complex multiplication.Modular form 15600.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
