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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 10080.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10080.bq1 | 10080bw3 | \([0, 0, 0, -590187, 174506866]\) | \(60910917333827912/3255076125\) | \(1214950653504000\) | \([2]\) | \(73728\) | \(1.9619\) | |
| 10080.bq2 | 10080bw2 | \([0, 0, 0, -190812, -29912384]\) | \(257307998572864/19456203375\) | \(58095911978496000\) | \([2]\) | \(73728\) | \(1.9619\) | |
| 10080.bq3 | 10080bw1 | \([0, 0, 0, -38937, 2406616]\) | \(139927692143296/27348890625\) | \(1275989841000000\) | \([2, 2]\) | \(36864\) | \(1.6153\) | \(\Gamma_0(N)\)-optimal |
| 10080.bq4 | 10080bw4 | \([0, 0, 0, 80133, 14242174]\) | \(152461584507448/322998046875\) | \(-120558375000000000\) | \([4]\) | \(73728\) | \(1.9619\) |
Rank
sage: E.rank()
The elliptic curves in class 10080.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 10080.bq do not have complex multiplication.Modular form 10080.2.a.bq
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.
