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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 49600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 49600.k1 | 49600ci2 | \([0, 1, 0, -1705633, 856816863]\) | \(133974081659809/192200\) | \(787251200000000\) | \([2]\) | \(442368\) | \(2.1294\) | |
| 49600.k2 | 49600ci1 | \([0, 1, 0, -105633, 13616863]\) | \(-31824875809/1240000\) | \(-5079040000000000\) | \([2]\) | \(221184\) | \(1.7828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 49600.k have rank \(1\).
Complex multiplication
The elliptic curves in class 49600.k do not have complex multiplication.Modular form 49600.2.a.k
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.
