Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 54720do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54720.o1 | 54720do1 | \([0, 0, 0, -33168, 2168408]\) | \(5405726654464/407253125\) | \(304012828800000\) | \([2]\) | \(184320\) | \(1.5243\) | \(\Gamma_0(N)\)-optimal |
| 54720.o2 | 54720do2 | \([0, 0, 0, 31812, 9628112]\) | \(298091207216/3525390625\) | \(-42107040000000000\) | \([2]\) | \(368640\) | \(1.8708\) |
Rank
sage: E.rank()
The elliptic curves in class 54720do have rank \(1\).
Complex multiplication
The elliptic curves in class 54720do do not have complex multiplication.Modular form 54720.2.a.do
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.
