Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 190440.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190440.bw1 | 190440g4 | \([0, 0, 0, -509427, -139944834]\) | \(132304644/5\) | \(552540994974720\) | \([2]\) | \(1576960\) | \(1.9148\) | |
190440.bw2 | 190440g2 | \([0, 0, 0, -33327, -1971054]\) | \(148176/25\) | \(690676243718400\) | \([2, 2]\) | \(788480\) | \(1.5683\) | |
190440.bw3 | 190440g1 | \([0, 0, 0, -9522, 328509]\) | \(55296/5\) | \(8633453046480\) | \([2]\) | \(394240\) | \(1.2217\) | \(\Gamma_0(N)\)-optimal |
190440.bw4 | 190440g3 | \([0, 0, 0, 61893, -11169306]\) | \(237276/625\) | \(-69067624371840000\) | \([2]\) | \(1576960\) | \(1.9148\) |
Rank
sage: E.rank()
The elliptic curves in class 190440.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 190440.bw do not have complex multiplication.Modular form 190440.2.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 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.