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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 148800.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148800.de1 | 148800kp3 | \([0, -1, 0, -10605633, 13297219137]\) | \(32208729120020809/658986840\) | \(2699210096640000000\) | \([2]\) | \(5308416\) | \(2.6562\) | |
| 148800.de2 | 148800kp2 | \([0, -1, 0, -685633, 192899137]\) | \(8702409880009/1120910400\) | \(4591248998400000000\) | \([2, 2]\) | \(2654208\) | \(2.3096\) | |
| 148800.de3 | 148800kp1 | \([0, -1, 0, -173633, -24700863]\) | \(141339344329/17141760\) | \(70212648960000000\) | \([2]\) | \(1327104\) | \(1.9630\) | \(\Gamma_0(N)\)-optimal |
| 148800.de4 | 148800kp4 | \([0, -1, 0, 1042367, 1006787137]\) | \(30579142915511/124675335000\) | \(-510670172160000000000\) | \([2]\) | \(5308416\) | \(2.6562\) |
Rank
sage: E.rank()
The elliptic curves in class 148800.de have rank \(1\).
Complex multiplication
The elliptic curves in class 148800.de do not have complex multiplication.Modular form 148800.2.a.de
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
