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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 203280ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.cj1 | 203280ct1 | \([0, -1, 0, -645, 2532]\) | \(1048576/525\) | \(14881112400\) | \([2]\) | \(134400\) | \(0.64473\) | \(\Gamma_0(N)\)-optimal |
| 203280.cj2 | 203280ct2 | \([0, -1, 0, 2380, 17052]\) | \(3286064/2205\) | \(-1000010753280\) | \([2]\) | \(268800\) | \(0.99131\) |
Rank
sage: E.rank()
The elliptic curves in class 203280ct have rank \(0\).
Complex multiplication
The elliptic curves in class 203280ct do not have complex multiplication.Modular form 203280.2.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.
