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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 101430.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.dn1 | 101430dr4 | \([1, -1, 1, -1329464408, 51516688731]\) | \(3029968325354577848895529/1753440696000000000000\) | \(150385806899460216000000000000\) | \([2]\) | \(106168320\) | \(4.2880\) | |
| 101430.dn2 | 101430dr2 | \([1, -1, 1, -914564993, 10645765390257]\) | \(986396822567235411402169/6336721794060000\) | \(543476048132687041260000\) | \([2]\) | \(35389440\) | \(3.7387\) | |
| 101430.dn3 | 101430dr1 | \([1, -1, 1, -56061473, 173052650481]\) | \(-227196402372228188089/19338934824115200\) | \(-1658625424136177961139200\) | \([2]\) | \(17694720\) | \(3.3922\) | \(\Gamma_0(N)\)-optimal |
| 101430.dn4 | 101430dr3 | \([1, -1, 1, 332364712, 6314936667]\) | \(47342661265381757089751/27397579603968000000\) | \(-2349784127421051568128000000\) | \([2]\) | \(53084160\) | \(3.9415\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.dn do not have complex multiplication.Modular form 101430.2.a.dn
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
