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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 17328.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17328.bb1 | 17328be3 | \([0, 1, 0, -2472248, -1497000108]\) | \(8671983378625/82308\) | \(15860745721233408\) | \([2]\) | \(311040\) | \(2.2709\) | |
| 17328.bb2 | 17328be4 | \([0, 1, 0, -2414488, -1570216684]\) | \(-8078253774625/846825858\) | \(-163183282352909918208\) | \([2]\) | \(622080\) | \(2.6174\) | |
| 17328.bb3 | 17328be1 | \([0, 1, 0, -46328, 277716]\) | \(57066625/32832\) | \(6326724055007232\) | \([2]\) | \(103680\) | \(1.7216\) | \(\Gamma_0(N)\)-optimal |
| 17328.bb4 | 17328be2 | \([0, 1, 0, 184712, 2403284]\) | \(3616805375/2105352\) | \(-405701180027338752\) | \([2]\) | \(207360\) | \(2.0681\) |
Rank
sage: E.rank()
The elliptic curves in class 17328.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 17328.bb do not have complex multiplication.Modular form 17328.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
