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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1980.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1980.f1 | 1980d4 | \([0, 0, 0, -2249967, 1299009526]\) | \(6749703004355978704/5671875\) | \(1058508000000\) | \([6]\) | \(13824\) | \(2.0429\) | |
| 1980.f2 | 1980d3 | \([0, 0, 0, -140592, 20306401]\) | \(-26348629355659264/24169921875\) | \(-281917968750000\) | \([6]\) | \(6912\) | \(1.6963\) | |
| 1980.f3 | 1980d2 | \([0, 0, 0, -28407, 1696894]\) | \(13584145739344/1195803675\) | \(223165665043200\) | \([2]\) | \(4608\) | \(1.4936\) | |
| 1980.f4 | 1980d1 | \([0, 0, 0, 1968, 123469]\) | \(72268906496/606436875\) | \(-7073479710000\) | \([2]\) | \(2304\) | \(1.1470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1980.f have rank \(0\).
Complex multiplication
The elliptic curves in class 1980.f do not have complex multiplication.Modular form 1980.2.a.f
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.
