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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1950.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1950.k1 | 1950g5 | \([1, 0, 1, -225376, -41200852]\) | \(81025909800741361/11088090\) | \(173251406250\) | \([2]\) | \(12288\) | \(1.5688\) | |
| 1950.k2 | 1950g4 | \([1, 0, 1, -21126, 1179148]\) | \(66730743078481/60937500\) | \(952148437500\) | \([2]\) | \(6144\) | \(1.2222\) | |
| 1950.k3 | 1950g3 | \([1, 0, 1, -14126, -640852]\) | \(19948814692561/231344100\) | \(3614751562500\) | \([2, 2]\) | \(6144\) | \(1.2222\) | |
| 1950.k4 | 1950g6 | \([1, 0, 1, -2876, -1630852]\) | \(-168288035761/73415764890\) | \(-1147121326406250\) | \([2]\) | \(12288\) | \(1.5688\) | |
| 1950.k5 | 1950g2 | \([1, 0, 1, -1626, 9148]\) | \(30400540561/15210000\) | \(237656250000\) | \([2, 2]\) | \(3072\) | \(0.87564\) | |
| 1950.k6 | 1950g1 | \([1, 0, 1, 374, 1148]\) | \(371694959/249600\) | \(-3900000000\) | \([2]\) | \(1536\) | \(0.52907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1950.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1950.k do not have complex multiplication.Modular form 1950.2.a.k
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
