Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 144400.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 144400.bd1 | 144400cj4 | \([0, 0, 0, -965675, -365241750]\) | \(132304644/5\) | \(3763670480000000\) | \([2]\) | \(1327104\) | \(2.0747\) | |
| 144400.bd2 | 144400cj2 | \([0, 0, 0, -63175, -5144250]\) | \(148176/25\) | \(4704588100000000\) | \([2, 2]\) | \(663552\) | \(1.7282\) | |
| 144400.bd3 | 144400cj1 | \([0, 0, 0, -18050, 857375]\) | \(55296/5\) | \(58807351250000\) | \([2]\) | \(331776\) | \(1.3816\) | \(\Gamma_0(N)\)-optimal |
| 144400.bd4 | 144400cj3 | \([0, 0, 0, 117325, -29150750]\) | \(237276/625\) | \(-470458810000000000\) | \([2]\) | \(1327104\) | \(2.0747\) |
Rank
sage: E.rank()
The elliptic curves in class 144400.bd have rank \(2\).
Complex multiplication
The elliptic curves in class 144400.bd do not have complex multiplication.Modular form 144400.2.a.bd
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.
