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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 45486.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45486.a1 | 45486v2 | \([1, -1, 0, -1944594, -1043238236]\) | \(23711636464489/363888\) | \(12480065596544112\) | \([2]\) | \(1474560\) | \(2.2240\) | |
45486.a2 | 45486v1 | \([1, -1, 0, -125154, -15254636]\) | \(6321363049/715008\) | \(24522234154612992\) | \([2]\) | \(737280\) | \(1.8775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45486.a have rank \(0\).
Complex multiplication
The elliptic curves in class 45486.a do not have complex multiplication.Modular form 45486.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.