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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 28050.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.dn1 | 28050dg2 | \([1, 0, 0, -3588, 52542]\) | \(326940373369/112003650\) | \(1750057031250\) | \([2]\) | \(49152\) | \(1.0512\) | |
28050.dn2 | 28050dg1 | \([1, 0, 0, 662, 5792]\) | \(2053225511/2098140\) | \(-32783437500\) | \([2]\) | \(24576\) | \(0.70460\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28050.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.dn do not have complex multiplication.Modular form 28050.2.a.dn
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.