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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 23520.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.bw1 | 23520u4 | \([0, 1, 0, -15876800, -24354934500]\) | \(7347751505995469192/72930375\) | \(4393055072448000\) | \([2]\) | \(737280\) | \(2.5778\) | |
| 23520.bw2 | 23520u3 | \([0, 1, 0, -1421800, -20383000]\) | \(5276930158229192/3050936350875\) | \(183777080700975552000\) | \([4]\) | \(737280\) | \(2.5778\) | |
| 23520.bw3 | 23520u1 | \([0, 1, 0, -993050, -380190000]\) | \(14383655824793536/45209390625\) | \(340405734249000000\) | \([2, 2]\) | \(368640\) | \(2.2313\) | \(\Gamma_0(N)\)-optimal |
| 23520.bw4 | 23520u2 | \([0, 1, 0, -576305, -701333697]\) | \(-43927191786304/415283203125\) | \(-200120949000000000000\) | \([2]\) | \(737280\) | \(2.5778\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.bw do not have complex multiplication.Modular form 23520.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
