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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 147030bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 147030.u4 | 147030bu1 | \([1, 0, 1, -4785239, 1154292986]\) | \(2510581756496128561/1333551278592000\) | \(6436797313469372928000\) | \([2]\) | \(11612160\) | \(2.8761\) | \(\Gamma_0(N)\)-optimal |
| 147030.u2 | 147030bu2 | \([1, 0, 1, -44209559, -112277360518]\) | \(1979758117698975186481/17510434929000000\) | \(84519524909211561000000\) | \([2, 2]\) | \(23224320\) | \(3.2227\) | |
| 147030.u3 | 147030bu3 | \([1, 0, 1, -13363679, -266050241494]\) | \(-54681655838565466801/6303365630859375000\) | \(-30425141957322708984375000\) | \([2]\) | \(46448640\) | \(3.5693\) | |
| 147030.u1 | 147030bu4 | \([1, 0, 1, -705844559, -7217972606518]\) | \(8057323694463985606146481/638717154543000\) | \(3082965710002543287000\) | \([2]\) | \(46448640\) | \(3.5693\) |
Rank
sage: E.rank()
The elliptic curves in class 147030bu have rank \(1\).
Complex multiplication
The elliptic curves in class 147030bu do not have complex multiplication.Modular form 147030.2.a.bu
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.
