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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 7920bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.y4 | 7920bl1 | \([0, 0, 0, 1968, -123469]\) | \(72268906496/606436875\) | \(-7073479710000\) | \([2]\) | \(9216\) | \(1.1470\) | \(\Gamma_0(N)\)-optimal |
| 7920.y3 | 7920bl2 | \([0, 0, 0, -28407, -1696894]\) | \(13584145739344/1195803675\) | \(223165665043200\) | \([2]\) | \(18432\) | \(1.4936\) | |
| 7920.y2 | 7920bl3 | \([0, 0, 0, -140592, -20306401]\) | \(-26348629355659264/24169921875\) | \(-281917968750000\) | \([2]\) | \(27648\) | \(1.6963\) | |
| 7920.y1 | 7920bl4 | \([0, 0, 0, -2249967, -1299009526]\) | \(6749703004355978704/5671875\) | \(1058508000000\) | \([2]\) | \(55296\) | \(2.0429\) |
Rank
sage: E.rank()
The elliptic curves in class 7920bl have rank \(1\).
Complex multiplication
The elliptic curves in class 7920bl do not have complex multiplication.Modular form 7920.2.a.bl
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 Cremona 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 Cremona labels.
