Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 485100.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.c1 | 485100c2 | \([0, 0, 0, -2235135, -739422250]\) | \(449955166736/174330387\) | \(478452514093402464000\) | \([2]\) | \(20643840\) | \(2.6670\) | \(\Gamma_0(N)\)-optimal* |
485100.c2 | 485100c1 | \([0, 0, 0, 443940, -83048875]\) | \(56409309184/50014503\) | \(-8579099832105726000\) | \([2]\) | \(10321920\) | \(2.3204\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.c have rank \(1\).
Complex multiplication
The elliptic curves in class 485100.c do not have complex multiplication.Modular form 485100.2.a.c
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.