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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 3150.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.bb1 | 3150w3 | \([1, -1, 1, -10505, -360503]\) | \(416832723/56000\) | \(17222625000000\) | \([2]\) | \(6912\) | \(1.2672\) | |
| 3150.bb2 | 3150w1 | \([1, -1, 1, -2630, 52497]\) | \(4767078987/6860\) | \(2894062500\) | \([2]\) | \(2304\) | \(0.71792\) | \(\Gamma_0(N)\)-optimal |
| 3150.bb3 | 3150w2 | \([1, -1, 1, -1880, 82497]\) | \(-1740992427/5882450\) | \(-2481658593750\) | \([2]\) | \(4608\) | \(1.0645\) | |
| 3150.bb4 | 3150w4 | \([1, -1, 1, 16495, -1926503]\) | \(1613964717/6125000\) | \(-1883724609375000\) | \([2]\) | \(13824\) | \(1.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.bb do not have complex multiplication.Modular form 3150.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
