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SageMath
E = EllipticCurve("ic1")
E.isogeny_class()
Elliptic curves in class 286650ic
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ic2 | 286650ic1 | \([1, -1, 0, -171117, -23638959]\) | \(3307949/468\) | \(78395594976562500\) | \([2]\) | \(3932160\) | \(1.9677\) | \(\Gamma_0(N)\)-optimal |
| 286650.ic1 | 286650ic2 | \([1, -1, 0, -722367, 212847291]\) | \(248858189/27378\) | \(4586142306128906250\) | \([2]\) | \(7864320\) | \(2.3142\) |
Rank
sage: E.rank()
The elliptic curves in class 286650ic have rank \(0\).
Complex multiplication
The elliptic curves in class 286650ic do not have complex multiplication.Modular form 286650.2.a.ic
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.
