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SageMath
E = EllipticCurve("hk1")
E.isogeny_class()
Elliptic curves in class 33600.hk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.hk1 | 33600dv2 | \([0, 1, 0, -5774833, -5341567537]\) | \(665567485783184/257298363\) | \(8233547616000000000\) | \([2]\) | \(1290240\) | \(2.5949\) | |
33600.hk2 | 33600dv1 | \([0, 1, 0, -307333, -109170037]\) | \(-1605176213504/1640558367\) | \(-3281116734000000000\) | \([2]\) | \(645120\) | \(2.2484\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33600.hk have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.hk do not have complex multiplication.Modular form 33600.2.a.hk
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.