Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 496860bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 496860.bg1 | 496860bg1 | \([0, -1, 0, -44165, -1297050]\) | \(1048576/525\) | \(4770101717144400\) | \([2]\) | \(2488320\) | \(1.7012\) | \(\Gamma_0(N)\)-optimal |
| 496860.bg2 | 496860bg2 | \([0, -1, 0, 162860, -10157720]\) | \(3286064/2205\) | \(-320550835392103680\) | \([2]\) | \(4976640\) | \(2.0478\) |
Rank
sage: E.rank()
The elliptic curves in class 496860bg have rank \(0\).
Complex multiplication
The elliptic curves in class 496860bg do not have complex multiplication.Modular form 496860.2.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 Cremona 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 Cremona labels.
