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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 147030.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 147030.be1 | 147030bn4 | \([1, 0, 1, -10937853, -13922732744]\) | \(29981943972267024529/4007065140000\) | \(19341338081338260000\) | \([2]\) | \(6451200\) | \(2.7199\) | |
| 147030.be2 | 147030bn3 | \([1, 0, 1, -4394173, 3404737208]\) | \(1943993954077461649/87266819409120\) | \(421220269325315098080\) | \([2]\) | \(6451200\) | \(2.7199\) | |
| 147030.be3 | 147030bn2 | \([1, 0, 1, -743773, -177035272]\) | \(9427227449071249/2652468249600\) | \(12802957619383526400\) | \([2, 2]\) | \(3225600\) | \(2.3733\) | |
| 147030.be4 | 147030bn1 | \([1, 0, 1, 121507, -18169864]\) | \(41102915774831/53367275520\) | \(-257593645785415680\) | \([2]\) | \(1612800\) | \(2.0268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147030.be have rank \(1\).
Complex multiplication
The elliptic curves in class 147030.be do not have complex multiplication.Modular form 147030.2.a.be
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.
