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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 11760.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.p1 | 11760bq7 | \([0, -1, 0, -1693456, -847656704]\) | \(1114544804970241/405\) | \(195165573120\) | \([2]\) | \(98304\) | \(1.9570\) | |
| 11760.p2 | 11760bq5 | \([0, -1, 0, -105856, -13214144]\) | \(272223782641/164025\) | \(79042057113600\) | \([2, 2]\) | \(49152\) | \(1.6104\) | |
| 11760.p3 | 11760bq8 | \([0, -1, 0, -86256, -18278784]\) | \(-147281603041/215233605\) | \(-103718987344465920\) | \([2]\) | \(98304\) | \(1.9570\) | |
| 11760.p4 | 11760bq4 | \([0, -1, 0, -62736, 6069120]\) | \(56667352321/15\) | \(7228354560\) | \([2]\) | \(24576\) | \(1.2638\) | |
| 11760.p5 | 11760bq3 | \([0, -1, 0, -7856, -121344]\) | \(111284641/50625\) | \(24395696640000\) | \([2, 2]\) | \(24576\) | \(1.2638\) | |
| 11760.p6 | 11760bq2 | \([0, -1, 0, -3936, 95040]\) | \(13997521/225\) | \(108425318400\) | \([2, 2]\) | \(12288\) | \(0.91725\) | |
| 11760.p7 | 11760bq1 | \([0, -1, 0, -16, 4096]\) | \(-1/15\) | \(-7228354560\) | \([2]\) | \(6144\) | \(0.57068\) | \(\Gamma_0(N)\)-optimal |
| 11760.p8 | 11760bq6 | \([0, -1, 0, 27424, -939840]\) | \(4733169839/3515625\) | \(-1694145600000000\) | \([2]\) | \(49152\) | \(1.6104\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.p have rank \(1\).
Complex multiplication
The elliptic curves in class 11760.p do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
