Show commands:
SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 87360du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.gp1 | 87360du1 | \([0, 1, 0, -283465, 57995063]\) | \(614983729942899136/35933625\) | \(147184128000\) | \([2]\) | \(522240\) | \(1.6077\) | \(\Gamma_0(N)\)-optimal |
| 87360.gp2 | 87360du2 | \([0, 1, 0, -282945, 58218975]\) | \(-76450685425962632/587722078125\) | \(-19258477056000000\) | \([2]\) | \(1044480\) | \(1.9543\) |
Rank
sage: E.rank()
The elliptic curves in class 87360du have rank \(1\).
Complex multiplication
The elliptic curves in class 87360du do not have complex multiplication.Modular form 87360.2.a.du
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.
