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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 140790bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140790.bb3 | 140790bu1 | \([1, 0, 1, -281588, 55382258]\) | \(52485860157121/2185297920\) | \(102809265893867520\) | \([2]\) | \(2211840\) | \(2.0293\) | \(\Gamma_0(N)\)-optimal |
| 140790.bb2 | 140790bu2 | \([1, 0, 1, -743668, -173070094]\) | \(966804247131841/284643590400\) | \(13391308481371142400\) | \([2, 2]\) | \(4423680\) | \(2.3759\) | |
| 140790.bb4 | 140790bu3 | \([1, 0, 1, 1999932, -1151986574]\) | \(18803907527146559/23071299329520\) | \(-1085409602771977707120\) | \([2]\) | \(8847360\) | \(2.7225\) | |
| 140790.bb1 | 140790bu4 | \([1, 0, 1, -10880548, -13813255822]\) | \(3027989442753063361/457426710000\) | \(21520042564881510000\) | \([2]\) | \(8847360\) | \(2.7225\) |
Rank
sage: E.rank()
The elliptic curves in class 140790bu have rank \(0\).
Complex multiplication
The elliptic curves in class 140790bu do not have complex multiplication.Modular form 140790.2.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.
