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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 22344.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22344.bb1 | 22344t4 | \([0, 1, 0, -29048392, -60269971168]\) | \(22501000029889239268/3620708343\) | \(436196061025901568\) | \([2]\) | \(1179648\) | \(2.7871\) | |
| 22344.bb2 | 22344t2 | \([0, 1, 0, -1821052, -936151840]\) | \(22174957026242512/278654127129\) | \(8392545127065528576\) | \([2, 2]\) | \(589824\) | \(2.4405\) | |
| 22344.bb3 | 22344t3 | \([0, 1, 0, -312832, -2438338960]\) | \(-28104147578308/21301741002339\) | \(-2566275611836601355264\) | \([2]\) | \(1179648\) | \(2.7871\) | |
| 22344.bb4 | 22344t1 | \([0, 1, 0, -213607, 14812622]\) | \(572616640141312/280535480757\) | \(528075500409284688\) | \([4]\) | \(294912\) | \(2.0940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22344.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 22344.bb do not have complex multiplication.Modular form 22344.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
