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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 71478.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71478.bl1 | 71478ct4 | \([1, -1, 1, -1143716, -470501899]\) | \(4824238966273/66\) | \(2263565518434\) | \([2]\) | \(884736\) | \(1.9266\) | |
| 71478.bl2 | 71478ct2 | \([1, -1, 1, -71546, -7324459]\) | \(1180932193/4356\) | \(149395324216644\) | \([2, 2]\) | \(442368\) | \(1.5800\) | |
| 71478.bl3 | 71478ct3 | \([1, -1, 1, -39056, -14030395]\) | \(-192100033/2371842\) | \(-81345754035962658\) | \([2]\) | \(884736\) | \(1.9266\) | |
| 71478.bl4 | 71478ct1 | \([1, -1, 1, -6566, 5285]\) | \(912673/528\) | \(18108524147472\) | \([2]\) | \(221184\) | \(1.2334\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71478.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 71478.bl do not have complex multiplication.Modular form 71478.2.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.
