Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 8820.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.x1 | 8820y1 | \([0, 0, 0, -249312, 47912641]\) | \(1248870793216/42525\) | \(58355268728400\) | \([2]\) | \(46080\) | \(1.7332\) | \(\Gamma_0(N)\)-optimal |
| 8820.x2 | 8820y2 | \([0, 0, 0, -238287, 52342486]\) | \(-68150496976/14467005\) | \(-317639398742426880\) | \([2]\) | \(92160\) | \(2.0797\) |
Rank
sage: E.rank()
The elliptic curves in class 8820.x have rank \(1\).
Complex multiplication
The elliptic curves in class 8820.x do not have complex multiplication.Modular form 8820.2.a.x
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.
