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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 11760.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.bw1 | 11760x5 | \([0, 1, 0, -156816, -23954316]\) | \(1770025017602/75\) | \(18070886400\) | \([2]\) | \(49152\) | \(1.4530\) | |
| 11760.bw2 | 11760x3 | \([0, 1, 0, -9816, -375516]\) | \(868327204/5625\) | \(677658240000\) | \([2, 2]\) | \(24576\) | \(1.1064\) | |
| 11760.bw3 | 11760x6 | \([0, 1, 0, -3936, -815340]\) | \(-27995042/1171875\) | \(-282357600000000\) | \([2]\) | \(49152\) | \(1.4530\) | |
| 11760.bw4 | 11760x2 | \([0, 1, 0, -996, 1980]\) | \(3631696/2025\) | \(60989241600\) | \([2, 2]\) | \(12288\) | \(0.75981\) | |
| 11760.bw5 | 11760x1 | \([0, 1, 0, -751, 7664]\) | \(24918016/45\) | \(84707280\) | \([2]\) | \(6144\) | \(0.41323\) | \(\Gamma_0(N)\)-optimal |
| 11760.bw6 | 11760x4 | \([0, 1, 0, 3904, 19620]\) | \(54607676/32805\) | \(-3952102855680\) | \([2]\) | \(24576\) | \(1.1064\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 11760.bw do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
