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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 151725.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151725.bg1 | 151725t4 | \([1, 0, 0, -812963, -282180708]\) | \(157551496201/13125\) | \(4950087392578125\) | \([2]\) | \(1966080\) | \(2.0554\) | |
| 151725.bg2 | 151725t2 | \([1, 0, 0, -54338, -3765333]\) | \(47045881/11025\) | \(4158073409765625\) | \([2, 2]\) | \(983040\) | \(1.7088\) | |
| 151725.bg3 | 151725t1 | \([1, 0, 0, -18213, 894792]\) | \(1771561/105\) | \(39600699140625\) | \([2]\) | \(491520\) | \(1.3622\) | \(\Gamma_0(N)\)-optimal |
| 151725.bg4 | 151725t3 | \([1, 0, 0, 126287, -23453458]\) | \(590589719/972405\) | \(-366742074741328125\) | \([2]\) | \(1966080\) | \(2.0554\) |
Rank
sage: E.rank()
The elliptic curves in class 151725.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 151725.bg do not have complex multiplication.Modular form 151725.2.a.bg
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.
