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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 160080ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.m1 | 160080ct1 | \([0, -1, 0, -591, -1170]\) | \(1429225682944/776638125\) | \(12426210000\) | \([2]\) | \(86016\) | \(0.62782\) | \(\Gamma_0(N)\)-optimal |
| 160080.m2 | 160080ct2 | \([0, -1, 0, 2284, -11520]\) | \(5144958608816/3172735575\) | \(-812220307200\) | \([2]\) | \(172032\) | \(0.97439\) |
Rank
sage: E.rank()
The elliptic curves in class 160080ct have rank \(0\).
Complex multiplication
The elliptic curves in class 160080ct do not have complex multiplication.Modular form 160080.2.a.ct
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.
