Show commands:
SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 19950.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19950.cy1 | 19950cw3 | \([1, 0, 0, -313600188, -2137557937008]\) | \(218289391029690300712901881/306514992000\) | \(4789296750000000\) | \([2]\) | \(2580480\) | \(3.1737\) | |
| 19950.cy2 | 19950cw4 | \([1, 0, 0, -20512188, -30121297008]\) | \(61085713691774408830201/10268551781250000000\) | \(160446121582031250000000\) | \([2]\) | \(2580480\) | \(3.1737\) | |
| 19950.cy3 | 19950cw2 | \([1, 0, 0, -19600188, -33399937008]\) | \(53294746224000958661881/1997017344000000\) | \(31203396000000000000\) | \([2, 2]\) | \(1290240\) | \(2.8271\) | |
| 19950.cy4 | 19950cw1 | \([1, 0, 0, -1168188, -572545008]\) | \(-11283450590382195961/2530373271552000\) | \(-39537082368000000000\) | \([4]\) | \(645120\) | \(2.4805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19950.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 19950.cy do not have complex multiplication.Modular form 19950.2.a.cy
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.
