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SageMath
sage: E = EllipticCurve("bo1")
sage: E.isogeny_class()
Elliptic curves in class 224400bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
224400.fm2 | 224400bo1 | [0, 1, 0, -4808, -105612] | [2] | 294912 | \(\Gamma_0(N)\)-optimal |
224400.fm1 | 224400bo2 | [0, 1, 0, -72808, -7585612] | [2] | 589824 |
Rank
sage: E.rank()
The elliptic curves in class 224400bo have rank \(0\).
Complex multiplication
The elliptic curves in class 224400bo do not have complex multiplication.Modular form 224400.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.