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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 248256.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248256.bb1 | 248256bb4 | \([0, 0, 0, -35748876, -82270038544]\) | \(26438903289204662017/11637\) | \(2223865331712\) | \([2]\) | \(8159232\) | \(2.6141\) | |
| 248256.bb2 | 248256bb3 | \([0, 0, 0, -2312076, -1191179536]\) | \(7152577607925217/931693026267\) | \(178049310038069870592\) | \([2]\) | \(8159232\) | \(2.6141\) | |
| 248256.bb3 | 248256bb2 | \([0, 0, 0, -2234316, -1285455760]\) | \(6454907876131057/135419769\) | \(25879120865132544\) | \([2, 2]\) | \(4079616\) | \(2.2675\) | |
| 248256.bb4 | 248256bb1 | \([0, 0, 0, -134796, -21544720]\) | \(-1417383186337/229051071\) | \(-43772341324087296\) | \([2]\) | \(2039808\) | \(1.9209\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248256.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 248256.bb do not have complex multiplication.Modular form 248256.2.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.
