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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 9702.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.n1 | 9702u4 | \([1, -1, 0, -6232662, -5987079050]\) | \(312196988566716625/25367712678\) | \(2175690315034582038\) | \([2]\) | \(221184\) | \(2.5638\) | |
9702.n2 | 9702u3 | \([1, -1, 0, -362952, -106803572]\) | \(-61653281712625/21875235228\) | \(-1876154071468110588\) | \([2]\) | \(110592\) | \(2.2172\) | |
9702.n3 | 9702u2 | \([1, -1, 0, -160092, 12405784]\) | \(5290763640625/2291573592\) | \(196539377971876632\) | \([2]\) | \(73728\) | \(2.0145\) | |
9702.n4 | 9702u1 | \([1, -1, 0, 33948, 1423120]\) | \(50447927375/39517632\) | \(-3389274007745472\) | \([2]\) | \(36864\) | \(1.6679\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.n have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.n do not have complex multiplication.Modular form 9702.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.