Show commands for:
SageMath
sage: E = EllipticCurve("cj1")
sage: E.isogeny_class()
Elliptic curves in class 19600.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
19600.cj1 | 19600h4 | [0, 0, 0, -366275, 85321250] | [2] | 98304 | |
19600.cj2 | 19600h3 | [0, 0, 0, -72275, -5916750] | [2] | 98304 | |
19600.cj3 | 19600h2 | [0, 0, 0, -23275, 1286250] | [2, 2] | 49152 | |
19600.cj4 | 19600h1 | [0, 0, 0, 1225, 85750] | [2] | 24576 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 19600.cj do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.