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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 215600cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.dv4 | 215600cv1 | \([0, 0, 0, -572075, -1762419750]\) | \(-2749884201/176619520\) | \(-1329863034142720000000\) | \([2]\) | \(7077888\) | \(2.7331\) | \(\Gamma_0(N)\)-optimal |
| 215600.dv3 | 215600cv2 | \([0, 0, 0, -25660075, -49705587750]\) | \(248158561089321/1859334400\) | \(13999925300838400000000\) | \([2, 2]\) | \(14155776\) | \(3.0796\) | |
| 215600.dv2 | 215600cv3 | \([0, 0, 0, -42908075, 25512940250]\) | \(1160306142246441/634128110000\) | \(4774690432856960000000000\) | \([2]\) | \(28311552\) | \(3.4262\) | |
| 215600.dv1 | 215600cv4 | \([0, 0, 0, -409820075, -3193286867750]\) | \(1010962818911303721/57392720\) | \(432140551377920000000\) | \([2]\) | \(28311552\) | \(3.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 215600cv have rank \(0\).
Complex multiplication
The elliptic curves in class 215600cv do not have complex multiplication.Modular form 215600.2.a.cv
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.
