Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 11970.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11970.ba1 | 11970ba3 | \([1, -1, 0, -1335339, -593058267]\) | \(361219316414914078129/378697617819360\) | \(276070563390313440\) | \([2]\) | \(245760\) | \(2.2638\) | |
| 11970.ba2 | 11970ba2 | \([1, -1, 0, -104139, -4298427]\) | \(171332100266282929/88068464870400\) | \(64201910890521600\) | \([2, 2]\) | \(122880\) | \(1.9172\) | |
| 11970.ba3 | 11970ba1 | \([1, -1, 0, -58059, 5350725]\) | \(29689921233686449/307510640640\) | \(224175257026560\) | \([2]\) | \(61440\) | \(1.5707\) | \(\Gamma_0(N)\)-optimal |
| 11970.ba4 | 11970ba4 | \([1, -1, 0, 389781, -33637275]\) | \(8983747840943130191/5865547515660000\) | \(-4275984138916140000\) | \([2]\) | \(245760\) | \(2.2638\) |
Rank
sage: E.rank()
The elliptic curves in class 11970.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 11970.ba do not have complex multiplication.Modular form 11970.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
