Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 35574.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.bu1 | 35574by3 | \([1, 1, 1, -477408, -126677055]\) | \(57736239625/255552\) | \(53262756076504128\) | \([2]\) | \(518400\) | \(2.0618\) | |
| 35574.bu2 | 35574by4 | \([1, 1, 1, -240248, -252276991]\) | \(-7357983625/127552392\) | \(-26584773126685122888\) | \([2]\) | \(1036800\) | \(2.4084\) | |
| 35574.bu3 | 35574by1 | \([1, 1, 1, -32733, 2136399]\) | \(18609625/1188\) | \(247605787545732\) | \([2]\) | \(172800\) | \(1.5125\) | \(\Gamma_0(N)\)-optimal |
| 35574.bu4 | 35574by2 | \([1, 1, 1, 26557, 9085187]\) | \(9938375/176418\) | \(-36769459450541202\) | \([2]\) | \(345600\) | \(1.8591\) |
Rank
sage: E.rank()
The elliptic curves in class 35574.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 35574.bu do not have complex multiplication.Modular form 35574.2.a.bu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
