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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9360.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.p1 | 9360bn5 | \([0, 0, 0, -1298163, -569300942]\) | \(81025909800741361/11088090\) | \(33108859330560\) | \([2]\) | \(98304\) | \(2.0065\) | |
| 9360.p2 | 9360bn4 | \([0, 0, 0, -121683, 16324882]\) | \(66730743078481/60937500\) | \(181958400000000\) | \([2]\) | \(49152\) | \(1.6600\) | |
| 9360.p3 | 9360bn3 | \([0, 0, 0, -81363, -8842862]\) | \(19948814692561/231344100\) | \(690789781094400\) | \([2, 2]\) | \(49152\) | \(1.6600\) | |
| 9360.p4 | 9360bn6 | \([0, 0, 0, -16563, -22541582]\) | \(-168288035761/73415764890\) | \(-219218299309301760\) | \([2]\) | \(98304\) | \(2.0065\) | |
| 9360.p5 | 9360bn2 | \([0, 0, 0, -9363, 128338]\) | \(30400540561/15210000\) | \(45416816640000\) | \([2, 2]\) | \(24576\) | \(1.3134\) | |
| 9360.p6 | 9360bn1 | \([0, 0, 0, 2157, 15442]\) | \(371694959/249600\) | \(-745301606400\) | \([2]\) | \(12288\) | \(0.96681\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9360.p have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.p do not have complex multiplication.Modular form 9360.2.a.p
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.
