Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5800.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5800.c1 | 5800e2 | \([0, 1, 0, -1428, -19952]\) | \(10070764688/707281\) | \(22632992000\) | \([2]\) | \(4608\) | \(0.73440\) | |
5800.c2 | 5800e1 | \([0, 1, 0, -1403, -20702]\) | \(152818608128/841\) | \(1682000\) | \([2]\) | \(2304\) | \(0.38782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5800.c have rank \(0\).
Complex multiplication
The elliptic curves in class 5800.c do not have complex multiplication.Modular form 5800.2.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.