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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4560.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.n1 | 4560d5 | \([0, -1, 0, -693120, 222337440]\) | \(17981241677724245762/16245\) | \(33269760\) | \([4]\) | \(16384\) | \(1.6386\) | |
| 4560.n2 | 4560d4 | \([0, -1, 0, -43320, 3484800]\) | \(8780093172522724/263900025\) | \(270233625600\) | \([2, 4]\) | \(8192\) | \(1.2920\) | |
| 4560.n3 | 4560d6 | \([0, -1, 0, -41520, 3785760]\) | \(-3865238121540962/764260336845\) | \(-1565205169858560\) | \([4]\) | \(16384\) | \(1.6386\) | |
| 4560.n4 | 4560d3 | \([0, -1, 0, -12320, -474000]\) | \(201971983086724/20447192475\) | \(20937925094400\) | \([2]\) | \(8192\) | \(1.2920\) | |
| 4560.n5 | 4560d2 | \([0, -1, 0, -2820, 50400]\) | \(9691367618896/1480325625\) | \(378963360000\) | \([2, 2]\) | \(4096\) | \(0.94545\) | |
| 4560.n6 | 4560d1 | \([0, -1, 0, 305, 4150]\) | \(195469297664/601171875\) | \(-9618750000\) | \([2]\) | \(2048\) | \(0.59887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.n have rank \(1\).
Complex multiplication
The elliptic curves in class 4560.n do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
