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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 179520.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.bc1 | 179520dt4 | \([0, -1, 0, -24122081, -44241294975]\) | \(5921450764096952391481/200074809015963750\) | \(52448410734680801280000\) | \([2]\) | \(14155776\) | \(3.1319\) | |
| 179520.bc2 | 179520dt2 | \([0, -1, 0, -3722081, 1809665025]\) | \(21754112339458491481/7199734626562500\) | \(1887367233945600000000\) | \([2, 2]\) | \(7077888\) | \(2.7853\) | |
| 179520.bc3 | 179520dt1 | \([0, -1, 0, -3352161, 2362991361]\) | \(15891267085572193561/3334993530000\) | \(874248543928320000\) | \([2]\) | \(3538944\) | \(2.4387\) | \(\Gamma_0(N)\)-optimal |
| 179520.bc4 | 179520dt3 | \([0, -1, 0, 10759199, 12441820801]\) | \(525440531549759128199/559322204589843750\) | \(-146622960000000000000000\) | \([2]\) | \(14155776\) | \(3.1319\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 179520.bc do not have complex multiplication.Modular form 179520.2.a.bc
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.
