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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 78144.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78144.bl1 | 78144ce4 | \([0, -1, 0, -358875297, -2616637778367]\) | \(19499096390516434897995817/15393430272\) | \(4035295385223168\) | \([2]\) | \(11796480\) | \(3.1990\) | |
| 78144.bl2 | 78144ce2 | \([0, -1, 0, -22429857, -40878778815]\) | \(4760617885089919932457/133756441657344\) | \(35063448641822785536\) | \([2, 2]\) | \(5898240\) | \(2.8525\) | |
| 78144.bl3 | 78144ce3 | \([0, -1, 0, -21528737, -44314749375]\) | \(-4209586785160189454377/801182513521564416\) | \(-210025188824596982267904\) | \([2]\) | \(11796480\) | \(3.1990\) | |
| 78144.bl4 | 78144ce1 | \([0, -1, 0, -1458337, -584100287]\) | \(1308451928740468777/194033737531392\) | \(50864780091429224448\) | \([2]\) | \(2949120\) | \(2.5059\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78144.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 78144.bl do not have complex multiplication.Modular form 78144.2.a.bl
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.
