Show commands:
SageMath
sage: E = EllipticCurve("fj1")
sage: E.isogeny_class()
Elliptic curves in class 369600.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.fj1 | 369600fj4 | \([0, -1, 0, -2957633, -1956796863]\) | \(1397097631688978/433125\) | \(887040000000000\) | \([2]\) | \(6291456\) | \(2.2307\) | |
| 369600.fj2 | 369600fj2 | \([0, -1, 0, -185633, -30256863]\) | \(690862540036/12006225\) | \(12294374400000000\) | \([2, 2]\) | \(3145728\) | \(1.8841\) | |
| 369600.fj3 | 369600fj1 | \([0, -1, 0, -23633, 685137]\) | \(5702413264/2525985\) | \(646652160000000\) | \([2]\) | \(1572864\) | \(1.5376\) | \(\Gamma_0(N)\)-optimal |
| 369600.fj4 | 369600fj3 | \([0, -1, 0, -5633, -86596863]\) | \(-9653618/1581886845\) | \(-3239704258560000000\) | \([2]\) | \(6291456\) | \(2.2307\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.fj have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.fj do not have complex multiplication.Modular form 369600.2.a.fj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
