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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 5550.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.bp1 | 5550bo2 | \([1, 0, 0, -9138, 177642]\) | \(43206601229/17964018\) | \(35085972656250\) | \([2]\) | \(12800\) | \(1.2963\) | |
5550.bp2 | 5550bo1 | \([1, 0, 0, -7888, 268892]\) | \(27790593389/11988\) | \(23414062500\) | \([2]\) | \(6400\) | \(0.94969\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5550.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 5550.bp do not have complex multiplication.Modular form 5550.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.