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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 20160.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.s1 | 20160cr3 | \([0, 0, 0, -60588, 5733072]\) | \(4767078987/6860\) | \(35396093214720\) | \([2]\) | \(55296\) | \(1.5022\) | |
| 20160.s2 | 20160cr4 | \([0, 0, 0, -43308, 9071568]\) | \(-1740992427/5882450\) | \(-30352149931622400\) | \([2]\) | \(110592\) | \(1.8488\) | |
| 20160.s3 | 20160cr1 | \([0, 0, 0, -2988, -55088]\) | \(416832723/56000\) | \(396361728000\) | \([2]\) | \(18432\) | \(0.95293\) | \(\Gamma_0(N)\)-optimal |
| 20160.s4 | 20160cr2 | \([0, 0, 0, 4692, -291632]\) | \(1613964717/6125000\) | \(-43352064000000\) | \([2]\) | \(36864\) | \(1.2995\) |
Rank
sage: E.rank()
The elliptic curves in class 20160.s have rank \(0\).
Complex multiplication
The elliptic curves in class 20160.s do not have complex multiplication.Modular form 20160.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
