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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 55440bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55440.er4 | 55440bs1 | \([0, 0, 0, 3273, 69046]\) | \(20777545136/23059575\) | \(-4303470124800\) | \([2]\) | \(65536\) | \(1.1107\) | \(\Gamma_0(N)\)-optimal |
55440.er3 | 55440bs2 | \([0, 0, 0, -18507, 648394]\) | \(939083699236/300155625\) | \(224064973440000\) | \([2, 2]\) | \(131072\) | \(1.4573\) | |
55440.er2 | 55440bs3 | \([0, 0, 0, -117507, -15013406]\) | \(120186986927618/4332064275\) | \(6467737306060800\) | \([2]\) | \(262144\) | \(1.8039\) | |
55440.er1 | 55440bs4 | \([0, 0, 0, -267987, 53388466]\) | \(1425631925916578/270703125\) | \(404157600000000\) | \([2]\) | \(262144\) | \(1.8039\) |
Rank
sage: E.rank()
The elliptic curves in class 55440bs have rank \(1\).
Complex multiplication
The elliptic curves in class 55440bs do not have complex multiplication.Modular form 55440.2.a.bs
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.