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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 58800.dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.dx1 | 58800w1 | \([0, -1, 0, -70408, 7213312]\) | \(7033666972/1215\) | \(6667920000000\) | \([2]\) | \(184320\) | \(1.4667\) | \(\Gamma_0(N)\)-optimal |
58800.dx2 | 58800w2 | \([0, -1, 0, -63408, 8697312]\) | \(-2568731006/1476225\) | \(-16203045600000000\) | \([2]\) | \(368640\) | \(1.8132\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.dx have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.dx do not have complex multiplication.Modular form 58800.2.a.dx
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.