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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4851.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4851.b1 | 4851j3 | \([1, -1, 1, -64616, 6331952]\) | \(347873904937/395307\) | \(33903947994147\) | \([2]\) | \(13824\) | \(1.5096\) | |
| 4851.b2 | 4851j2 | \([1, -1, 1, -5081, 45056]\) | \(169112377/88209\) | \(7565343767289\) | \([2, 2]\) | \(6912\) | \(1.1631\) | |
| 4851.b3 | 4851j1 | \([1, -1, 1, -2876, -58138]\) | \(30664297/297\) | \(25472537937\) | \([2]\) | \(3456\) | \(0.81648\) | \(\Gamma_0(N)\)-optimal |
| 4851.b4 | 4851j4 | \([1, -1, 1, 19174, 336116]\) | \(9090072503/5845851\) | \(-501375964213971\) | \([2]\) | \(13824\) | \(1.5096\) |
Rank
sage: E.rank()
The elliptic curves in class 4851.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4851.b do not have complex multiplication.Modular form 4851.2.a.b
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.
