Show commands:
SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 243936.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243936.cg1 | 243936cg2 | \([0, 0, 0, -36300, 2512928]\) | \(1000000/63\) | \(333260726464512\) | \([2]\) | \(716800\) | \(1.5377\) | |
243936.cg2 | 243936cg1 | \([0, 0, 0, 1815, 165044]\) | \(8000/147\) | \(-12150130652352\) | \([2]\) | \(358400\) | \(1.1911\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 243936.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 243936.cg do not have complex multiplication.Modular form 243936.2.a.cg
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.