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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 270480.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.bl1 | 270480bl3 | \([0, -1, 0, -28945358416, 1895410409375680]\) | \(5565604209893236690185614401/229307220930246900000\) | \(110500926403471841436057600000\) | \([2]\) | \(707788800\) | \(4.6543\) | |
| 270480.bl2 | 270480bl4 | \([0, -1, 0, -8824531536, -294238983219264]\) | \(157706830105239346386477121/13650704956054687500000\) | \(6578142361087500000000000000000\) | \([2]\) | \(707788800\) | \(4.6543\) | |
| 270480.bl3 | 270480bl2 | \([0, -1, 0, -1897358416, 26566716575680]\) | \(1567558142704512417614401/274462175610000000000\) | \(132260661241204285440000000000\) | \([2, 2]\) | \(353894400\) | \(4.3077\) | |
| 270480.bl4 | 270480bl1 | \([0, -1, 0, 226089904, 2378092072896]\) | \(2652277923951208297919/6605028468326400000\) | \(-3182899176530463267225600000\) | \([2]\) | \(176947200\) | \(3.9611\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.bl do not have complex multiplication.Modular form 270480.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
