Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 302016.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302016.cj1 | 302016cj2 | \([0, -1, 0, -47593, -1738295]\) | \(1643032000/767637\) | \(5570214999478272\) | \([2]\) | \(1638400\) | \(1.7158\) | |
302016.cj2 | 302016cj1 | \([0, -1, 0, -39728, -3032874]\) | \(61162984000/41067\) | \(4656172517568\) | \([2]\) | \(819200\) | \(1.3692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 302016.cj do not have complex multiplication.Modular form 302016.2.a.cj
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.