Show commands for:
SageMath
sage: E = EllipticCurve("194145.d1")
sage: E.isogeny_class()
Elliptic curves in class 194145j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
194145.d3 | 194145j1 | [1, 1, 1, -4661, -117982] | [2] | 322560 | \(\Gamma_0(N)\)-optimal |
194145.d2 | 194145j2 | [1, 1, 1, -13906, 481094] | [2, 2] | 645120 | |
194145.d1 | 194145j3 | [1, 1, 1, -208051, 36436748] | [2] | 1290240 | |
194145.d4 | 194145j4 | [1, 1, 1, 32319, 3051204] | [2] | 1290240 |
Rank
sage: E.rank()
The elliptic curves in class 194145j have rank \(0\).
Modular form 194145.2.a.d
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 Cremona 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 Cremona labels.