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SageMath
sage: E = EllipticCurve("225.a1")
sage: E.isogeny_class()
Elliptic curves in class 225.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
225.a1 | 225e1 | [0, 0, 1, -75, 256] | [] | 48 | \(\Gamma_0(N)\)-optimal |
225.a2 | 225e2 | [0, 0, 1, 375, -12344] | [] | 240 |
Rank
sage: E.rank()
The elliptic curves in class 225.a have rank \(1\).
Modular form 225.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.