Show commands:
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 | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.cj1 | 19600h4 | \([0, 0, 0, -366275, 85321250]\) | \(1443468546/7\) | \(26353376000000\) | \([2]\) | \(98304\) | \(1.7756\) | |
| 19600.cj2 | 19600h3 | \([0, 0, 0, -72275, -5916750]\) | \(11090466/2401\) | \(9039207968000000\) | \([2]\) | \(98304\) | \(1.7756\) | |
| 19600.cj3 | 19600h2 | \([0, 0, 0, -23275, 1286250]\) | \(740772/49\) | \(92236816000000\) | \([2, 2]\) | \(49152\) | \(1.4291\) | |
| 19600.cj4 | 19600h1 | \([0, 0, 0, 1225, 85750]\) | \(432/7\) | \(-3294172000000\) | \([2]\) | \(24576\) | \(1.0825\) | \(\Gamma_0(N)\)-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.
