Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 361920p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.p2 | 361920p1 | \([0, -1, 0, -73581, -7535475]\) | \(43025578182363136/787373218125\) | \(806270175360000\) | \([2]\) | \(2359296\) | \(1.6551\) | \(\Gamma_0(N)\)-optimal |
| 361920.p1 | 361920p2 | \([0, -1, 0, -1172081, -488019375]\) | \(10868685473848063696/3741545925\) | \(61301488435200\) | \([2]\) | \(4718592\) | \(2.0017\) |
Rank
sage: E.rank()
The elliptic curves in class 361920p have rank \(1\).
Complex multiplication
The elliptic curves in class 361920p do not have complex multiplication.Modular form 361920.2.a.p
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.
