Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 20800bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20800.y2 | 20800bk1 | \([0, -1, 0, -333, 2287]\) | \(163840/13\) | \(325000000\) | \([]\) | \(8640\) | \(0.37687\) | \(\Gamma_0(N)\)-optimal |
| 20800.y1 | 20800bk2 | \([0, -1, 0, -5333, -147713]\) | \(671088640/2197\) | \(54925000000\) | \([]\) | \(25920\) | \(0.92617\) |
Rank
sage: E.rank()
The elliptic curves in class 20800bk have rank \(0\).
Complex multiplication
The elliptic curves in class 20800bk do not have complex multiplication.Modular form 20800.2.a.bk
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
