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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 176400.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.dn1 | 176400n2 | \([0, 0, 0, -636675375, 6181303756250]\) | \(665567485783184/257298363\) | \(11033741267079961500000000\) | \([2]\) | \(61931520\) | \(3.7706\) | |
176400.dn2 | 176400n1 | \([0, 0, 0, -33883500, 126259371875]\) | \(-1605176213504/1640558367\) | \(-4397010231615137718750000\) | \([2]\) | \(30965760\) | \(3.4241\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.dn do not have complex multiplication.Modular form 176400.2.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.