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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 124950.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.bb1 | 124950t4 | \([1, 1, 0, -6221800, -5975999000]\) | \(14489843500598257/6246072\) | \(11481939448875000\) | \([2]\) | \(4718592\) | \(2.4242\) | |
| 124950.bb2 | 124950t3 | \([1, 1, 0, -831800, 153999000]\) | \(34623662831857/14438442312\) | \(26541692180695125000\) | \([2]\) | \(4718592\) | \(2.4242\) | |
| 124950.bb3 | 124950t2 | \([1, 1, 0, -390800, -92520000]\) | \(3590714269297/73410624\) | \(134948226609000000\) | \([2, 2]\) | \(2359296\) | \(2.0777\) | |
| 124950.bb4 | 124950t1 | \([1, 1, 0, 1200, -4320000]\) | \(103823/4386816\) | \(-8064133056000000\) | \([2]\) | \(1179648\) | \(1.7311\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 124950.bb do not have complex multiplication.Modular form 124950.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
