Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 363258.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363258.bt1 | 363258bt3 | \([1, -1, 1, -9186860, 10719926425]\) | \(-545407363875/14\) | \(-2201060604093498\) | \([]\) | \(9710280\) | \(2.4602\) | |
| 363258.bt2 | 363258bt2 | \([1, -1, 1, -105410, 16892713]\) | \(-7414875/2744\) | \(-47934208711369512\) | \([]\) | \(3236760\) | \(1.9109\) | |
| 363258.bt3 | 363258bt1 | \([1, -1, 1, 9910, -236151]\) | \(4492125/3584\) | \(-85881956203008\) | \([]\) | \(1078920\) | \(1.3616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363258.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 363258.bt do not have complex multiplication.Modular form 363258.2.a.bt
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
