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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 151008.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151008.be1 | 151008b4 | \([0, 1, 0, -453064, -117529348]\) | \(11339065490696/351\) | \(318370770432\) | \([2]\) | \(983040\) | \(1.7117\) | |
| 151008.be2 | 151008b2 | \([0, 1, 0, -44689, 504095]\) | \(1360251712/771147\) | \(5595684661112832\) | \([2]\) | \(983040\) | \(1.7117\) | |
| 151008.be3 | 151008b1 | \([0, 1, 0, -28354, -1838344]\) | \(22235451328/123201\) | \(13968517552704\) | \([2, 2]\) | \(491520\) | \(1.3651\) | \(\Gamma_0(N)\)-optimal |
| 151008.be4 | 151008b3 | \([0, 1, 0, -12624, -3851784]\) | \(-245314376/6908733\) | \(-6266491874413056\) | \([2]\) | \(983040\) | \(1.7117\) |
Rank
sage: E.rank()
The elliptic curves in class 151008.be have rank \(2\).
Complex multiplication
The elliptic curves in class 151008.be do not have complex multiplication.Modular form 151008.2.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.
