Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 5520.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5520.bg1 | 5520be2 | \([0, 1, 0, -50752920, 137408357268]\) | \(3529773792266261468365081/50841342773437500000\) | \(208246140000000000000000\) | \([2]\) | \(829440\) | \(3.2785\) | |
5520.bg2 | 5520be1 | \([0, 1, 0, -364440, 5813802900]\) | \(-1306902141891515161/3564268498800000000\) | \(-14599243771084800000000\) | \([2]\) | \(414720\) | \(2.9319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.bg do not have complex multiplication.Modular form 5520.2.a.bg
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.