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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 85800.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.x1 | 85800br4 | \([0, -1, 0, -1373008, 619696012]\) | \(8945265872486162/804375\) | \(25740000000000\) | \([2]\) | \(884736\) | \(2.0114\) | |
| 85800.x2 | 85800br3 | \([0, -1, 0, -151008, -6851988]\) | \(11900808771122/6243874065\) | \(199803970080000000\) | \([2]\) | \(884736\) | \(2.0114\) | |
| 85800.x3 | 85800br2 | \([0, -1, 0, -86008, 9658012]\) | \(4397697224644/41409225\) | \(662547600000000\) | \([2, 2]\) | \(442368\) | \(1.6648\) | |
| 85800.x4 | 85800br1 | \([0, -1, 0, -1508, 363012]\) | \(-94875856/14137695\) | \(-56550780000000\) | \([4]\) | \(221184\) | \(1.3182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85800.x have rank \(1\).
Complex multiplication
The elliptic curves in class 85800.x do not have complex multiplication.Modular form 85800.2.a.x
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.
