Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3600.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.c1 | 3600j2 | \([0, 0, 0, -7875, -268750]\) | \(1000188\) | \(54000000000\) | \([2]\) | \(5120\) | \(0.97879\) | |
3600.c2 | 3600j1 | \([0, 0, 0, -375, -6250]\) | \(-432\) | \(-13500000000\) | \([2]\) | \(2560\) | \(0.63221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3600.c have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.c do not have complex multiplication.Modular form 3600.2.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.