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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 116160.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.be1 | 116160fb4 | \([0, -1, 0, -25555361, 49733101761]\) | \(15897679904620804/2475\) | \(287350028697600\) | \([2]\) | \(3932160\) | \(2.6209\) | |
| 116160.be2 | 116160fb6 | \([0, -1, 0, -13552161, -18830105919]\) | \(1185450336504002/26043266205\) | \(6047299629402817167360\) | \([2]\) | \(7864320\) | \(2.9675\) | |
| 116160.be3 | 116160fb3 | \([0, -1, 0, -1839361, 526467361]\) | \(5927735656804/2401490025\) | \(278815445495252582400\) | \([2, 2]\) | \(3932160\) | \(2.6209\) | |
| 116160.be4 | 116160fb2 | \([0, -1, 0, -1597361, 777324561]\) | \(15529488955216/6125625\) | \(177797830256640000\) | \([2, 2]\) | \(1966080\) | \(2.2743\) | |
| 116160.be5 | 116160fb1 | \([0, -1, 0, -84861, 15932061]\) | \(-37256083456/38671875\) | \(-70153815600000000\) | \([2]\) | \(983040\) | \(1.9278\) | \(\Gamma_0(N)\)-optimal |
| 116160.be6 | 116160fb5 | \([0, -1, 0, 6001439, 3824307841]\) | \(102949393183198/86815346805\) | \(-20158700925906138562560\) | \([2]\) | \(7864320\) | \(2.9675\) |
Rank
sage: E.rank()
The elliptic curves in class 116160.be have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.be do not have complex multiplication.Modular form 116160.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
