Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 253575.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253575.bb1 | 253575bb3 | \([1, -1, 1, -1363655, 613122472]\) | \(209267191953/55223\) | \(74004101562234375\) | \([2]\) | \(3932160\) | \(2.2213\) | |
| 253575.bb2 | 253575bb2 | \([1, -1, 1, -95780, 7078222]\) | \(72511713/25921\) | \(34736619100640625\) | \([2, 2]\) | \(1966080\) | \(1.8748\) | |
| 253575.bb3 | 253575bb1 | \([1, -1, 1, -40655, -3064778]\) | \(5545233/161\) | \(215755398140625\) | \([2]\) | \(983040\) | \(1.5282\) | \(\Gamma_0(N)\)-optimal |
| 253575.bb4 | 253575bb4 | \([1, -1, 1, 290095, 49524472]\) | \(2014698447/1958887\) | \(-2625095929176984375\) | \([2]\) | \(3932160\) | \(2.2213\) |
Rank
sage: E.rank()
The elliptic curves in class 253575.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 253575.bb do not have complex multiplication.Modular form 253575.2.a.bb
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.
