Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 102960.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.do1 | 102960ei4 | \([0, 0, 0, -3802107, 2853544106]\) | \(2035678735521204409/141376950\) | \(422149310668800\) | \([2]\) | \(1179648\) | \(2.2605\) | |
| 102960.do2 | 102960ei3 | \([0, 0, 0, -406587, -26598166]\) | \(2489411558640889/1338278906250\) | \(3996079401600000000\) | \([2]\) | \(1179648\) | \(2.2605\) | |
| 102960.do3 | 102960ei2 | \([0, 0, 0, -238107, 44399306]\) | \(499980107400409/4140922500\) | \(12364728330240000\) | \([2, 2]\) | \(589824\) | \(1.9139\) | |
| 102960.do4 | 102960ei1 | \([0, 0, 0, -4827, 1615754]\) | \(-4165509529/375289200\) | \(-1120607546572800\) | \([2]\) | \(294912\) | \(1.5673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.do have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.do do not have complex multiplication.Modular form 102960.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
