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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1350.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1350.k1 | 1350h2 | \([1, -1, 0, -11367, 444541]\) | \(68450475/4096\) | \(9720000000000\) | \([]\) | \(4320\) | \(1.2448\) | |
| 1350.k2 | 1350h1 | \([1, -1, 0, -1992, -33584]\) | \(3316275/16\) | \(4218750000\) | \([]\) | \(1440\) | \(0.69554\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.k do not have complex multiplication.Modular form 1350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
