Show commands:
SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 43560.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43560.ce1 | 43560bb2 | \([0, 0, 0, -1869087, 646724914]\) | \(2184181167184/717482205\) | \(237210953237757861120\) | \([2]\) | \(1474560\) | \(2.6126\) | |
| 43560.ce2 | 43560bb1 | \([0, 0, 0, 336138, 69397009]\) | \(203269830656/218317275\) | \(-4511196283869831600\) | \([2]\) | \(737280\) | \(2.2661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43560.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 43560.ce do not have complex multiplication.Modular form 43560.2.a.ce
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.
