Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1287.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1287.c1 | 1287b2 | \([1, -1, 0, -16188, 779849]\) | \(23835655373139/584043889\) | \(11495735867187\) | \([2]\) | \(2880\) | \(1.2900\) | |
1287.c2 | 1287b1 | \([1, -1, 0, 147, 38240]\) | \(17779581/32166277\) | \(-633128830191\) | \([2]\) | \(1440\) | \(0.94346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1287.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1287.c do not have complex multiplication.Modular form 1287.2.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.