Show commands:
SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 198550cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
198550.z1 | 198550cu1 | \([1, 0, 1, -798901, -277535552]\) | \(-76711450249/851840\) | \(-626180676110000000\) | \([]\) | \(4245696\) | \(2.2297\) | \(\Gamma_0(N)\)-optimal |
198550.z2 | 198550cu2 | \([1, 0, 1, 2675724, -1438060302]\) | \(2882081488391/2883584000\) | \(-2119699214336000000000\) | \([]\) | \(12737088\) | \(2.7791\) |
Rank
sage: E.rank()
The elliptic curves in class 198550cu have rank \(1\).
Complex multiplication
The elliptic curves in class 198550cu do not have complex multiplication.Modular form 198550.2.a.cu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.