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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 203840.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203840.cy1 | 203840bv1 | \([0, 0, 0, -2650508, 1660882832]\) | \(267080942160036/1990625\) | \(15348206182400000\) | \([2]\) | \(3440640\) | \(2.2818\) | \(\Gamma_0(N)\)-optimal |
203840.cy2 | 203840bv2 | \([0, 0, 0, -2595628, 1732951248]\) | \(-125415986034978/11552734375\) | \(-178148821760000000000\) | \([2]\) | \(6881280\) | \(2.6283\) |
Rank
sage: E.rank()
The elliptic curves in class 203840.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 203840.cy do not have complex multiplication.Modular form 203840.2.a.cy
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.