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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 17424bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.by3 | 17424bw1 | \([0, 0, 0, -113619, 14617042]\) | \(30664297/297\) | \(1571086281904128\) | \([2]\) | \(92160\) | \(1.7356\) | \(\Gamma_0(N)\)-optimal |
| 17424.by2 | 17424bw2 | \([0, 0, 0, -200739, -10874270]\) | \(169112377/88209\) | \(466612625725526016\) | \([2, 2]\) | \(184320\) | \(2.0822\) | |
| 17424.by1 | 17424bw3 | \([0, 0, 0, -2552979, -1568527598]\) | \(347873904937/395307\) | \(2091115841214394368\) | \([2]\) | \(368640\) | \(2.4288\) | |
| 17424.by4 | 17424bw4 | \([0, 0, 0, 757581, -84664910]\) | \(9090072503/5845851\) | \(-30923691286718951424\) | \([2]\) | \(368640\) | \(2.4288\) |
Rank
sage: E.rank()
The elliptic curves in class 17424bw have rank \(0\).
Complex multiplication
The elliptic curves in class 17424bw do not have complex multiplication.Modular form 17424.2.a.bw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
