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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 374790bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374790.bm3 | 374790bm1 | \([1, 0, 1, -12994, -554044]\) | \(273359449/9360\) | \(8307034454160\) | \([2]\) | \(983040\) | \(1.2509\) | \(\Gamma_0(N)\)-optimal |
| 374790.bm2 | 374790bm2 | \([1, 0, 1, -32214, 1460212]\) | \(4165509529/1368900\) | \(1214903788920900\) | \([2, 2]\) | \(1966080\) | \(1.5975\) | |
| 374790.bm1 | 374790bm3 | \([1, 0, 1, -464664, 121854292]\) | \(12501706118329/2570490\) | \(2281319336973690\) | \([2]\) | \(3932160\) | \(1.9440\) | |
| 374790.bm4 | 374790bm4 | \([1, 0, 1, 92716, 10055396]\) | \(99317171591/106616250\) | \(-94622314329416250\) | \([2]\) | \(3932160\) | \(1.9440\) |
Rank
sage: E.rank()
The elliptic curves in class 374790bm have rank \(0\).
Complex multiplication
The elliptic curves in class 374790bm do not have complex multiplication.Modular form 374790.2.a.bm
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 Cremona 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 Cremona labels.
