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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 69360.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.n1 | 69360cc8 | \([0, -1, 0, -9987936, 12152923200]\) | \(1114544804970241/405\) | \(40041330462720\) | \([2]\) | \(1310720\) | \(2.4006\) | |
| 69360.n2 | 69360cc6 | \([0, -1, 0, -624336, 189987840]\) | \(272223782641/164025\) | \(16216738837401600\) | \([2, 2]\) | \(655360\) | \(2.0541\) | |
| 69360.n3 | 69360cc7 | \([0, -1, 0, -508736, 262399680]\) | \(-147281603041/215233605\) | \(-21279604702438379520\) | \([2]\) | \(1310720\) | \(2.4006\) | |
| 69360.n4 | 69360cc4 | \([0, -1, 0, -370016, -86508864]\) | \(56667352321/15\) | \(1483012239360\) | \([2]\) | \(327680\) | \(1.7075\) | |
| 69360.n5 | 69360cc3 | \([0, -1, 0, -46336, 1791040]\) | \(111284641/50625\) | \(5005166307840000\) | \([2, 2]\) | \(327680\) | \(1.7075\) | |
| 69360.n6 | 69360cc2 | \([0, -1, 0, -23216, -1334784]\) | \(13997521/225\) | \(22245183590400\) | \([2, 2]\) | \(163840\) | \(1.3609\) | |
| 69360.n7 | 69360cc1 | \([0, -1, 0, -96, -58560]\) | \(-1/15\) | \(-1483012239360\) | \([2]\) | \(81920\) | \(1.0143\) | \(\Gamma_0(N)\)-optimal |
| 69360.n8 | 69360cc5 | \([0, -1, 0, 161744, 13277056]\) | \(4733169839/3515625\) | \(-347580993600000000\) | \([2]\) | \(655360\) | \(2.0541\) |
Rank
sage: E.rank()
The elliptic curves in class 69360.n have rank \(2\).
Complex multiplication
The elliptic curves in class 69360.n do not have complex multiplication.Modular form 69360.2.a.n
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
