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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 10608b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.f2 | 10608b1 | \([0, -1, 0, -783, 8586]\) | \(3322336000000/51429573\) | \(822873168\) | \([2]\) | \(4608\) | \(0.51195\) | \(\Gamma_0(N)\)-optimal |
| 10608.f1 | 10608b2 | \([0, -1, 0, -1548, -10080]\) | \(1603530178000/738501777\) | \(189056454912\) | \([2]\) | \(9216\) | \(0.85852\) |
Rank
sage: E.rank()
The elliptic curves in class 10608b have rank \(0\).
Complex multiplication
The elliptic curves in class 10608b do not have complex multiplication.Modular form 10608.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
