Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 188760.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.bl1 | 188760y2 | \([0, -1, 0, -1389120, 604809900]\) | \(61387394182/2851875\) | \(13771923601962240000\) | \([2]\) | \(3446784\) | \(2.4337\) | |
188760.bl2 | 188760y1 | \([0, -1, 0, 48360, 36142812]\) | \(5180116/236925\) | \(-572064518850739200\) | \([2]\) | \(1723392\) | \(2.0871\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.bl do not have complex multiplication.Modular form 188760.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.