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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 5520.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5520.x1 | 5520ba4 | \([0, 1, 0, -22118576, 40031686740]\) | \(292169767125103365085489/72534787200\) | \(297102488371200\) | \([4]\) | \(172032\) | \(2.5928\) | |
5520.x2 | 5520ba3 | \([0, 1, 0, -1618096, 397291604]\) | \(114387056741228939569/49503729150000000\) | \(202767274598400000000\) | \([2]\) | \(172032\) | \(2.5928\) | |
5520.x3 | 5520ba2 | \([0, 1, 0, -1382576, 624992340]\) | \(71356102305927901489/35540674560000\) | \(145574602997760000\) | \([2, 2]\) | \(86016\) | \(2.2462\) | |
5520.x4 | 5520ba1 | \([0, 1, 0, -71856, 13148244]\) | \(-10017490085065009/12502381363200\) | \(-51209754063667200\) | \([2]\) | \(43008\) | \(1.8996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.x have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.x do not have complex multiplication.Modular form 5520.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.