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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 212160.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.eb1 | 212160fg4 | \([0, 1, 0, -24147841, -45681664801]\) | \(5940441603429810927841/3044264109120\) | \(798035570621153280\) | \([2]\) | \(14155776\) | \(2.7673\) | |
| 212160.eb2 | 212160fg2 | \([0, 1, 0, -1517441, -706007841]\) | \(1474074790091785441/32813650022400\) | \(8601901471472025600\) | \([2, 2]\) | \(7077888\) | \(2.4207\) | |
| 212160.eb3 | 212160fg1 | \([0, 1, 0, -206721, 19868895]\) | \(3726830856733921/1501644718080\) | \(393647152976363520\) | \([2]\) | \(3538944\) | \(2.0741\) | \(\Gamma_0(N)\)-optimal |
| 212160.eb4 | 212160fg3 | \([0, 1, 0, 141439, -2165490465]\) | \(1193680917131039/7728836230440000\) | \(-2026068044792463360000\) | \([2]\) | \(14155776\) | \(2.7673\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.eb do not have complex multiplication.Modular form 212160.2.a.eb
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.
