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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 219024bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 219024.bq3 | 219024bf1 | \([0, 0, 0, -12675, -575614]\) | \(-140625/8\) | \(-12811355062272\) | \([]\) | \(331776\) | \(1.2720\) | \(\Gamma_0(N)\)-optimal |
| 219024.bq4 | 219024bf2 | \([0, 0, 0, 68445, -1067742]\) | \(3375/2\) | \(-21013825140891648\) | \([]\) | \(995328\) | \(1.8213\) | |
| 219024.bq2 | 219024bf3 | \([0, 0, 0, -256035, 101294882]\) | \(-1159088625/2097152\) | \(-3358419861444231168\) | \([]\) | \(2322432\) | \(2.2450\) | |
| 219024.bq1 | 219024bf4 | \([0, 0, 0, -26214435, 51660561186]\) | \(-189613868625/128\) | \(-1344884809017065472\) | \([]\) | \(6967296\) | \(2.7943\) |
Rank
sage: E.rank()
The elliptic curves in class 219024bf have rank \(0\).
Complex multiplication
The elliptic curves in class 219024bf do not have complex multiplication.Modular form 219024.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
