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SageMath
E = EllipticCurve("sb1")
E.isogeny_class()
Elliptic curves in class 705600.sb
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.sb1 | \([0, 0, 0, -39900, 2842000]\) | \(109744/9\) | \(576108288000000\) | \([2]\) | \(3145728\) | \(1.5748\) |
| 705600.sb2 | \([0, 0, 0, -8400, -245000]\) | \(16384/3\) | \(12002256000000\) | \([2]\) | \(1572864\) | \(1.2282\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.sb have rank \(2\).
Complex multiplication
The elliptic curves in class 705600.sb do not have complex multiplication.Modular form 705600.2.a.sb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
