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SageMath
E = EllipticCurve("lc1")
E.isogeny_class()
Elliptic curves in class 346560lc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.lc4 | 346560lc1 | \([0, 1, 0, 84941375, 1808469396383]\) | \(5495662324535111/117739817533440\) | \(-1452061083471690271461212160\) | \([2]\) | \(154828800\) | \(3.8922\) | \(\Gamma_0(N)\)-optimal |
346560.lc3 | 346560lc2 | \([0, 1, 0, -1807738305, 28020947356575]\) | \(52974743974734147769/3152005008998400\) | \(38873032966731898707089817600\) | \([2, 2]\) | \(309657600\) | \(4.2388\) | |
346560.lc1 | 346560lc3 | \([0, 1, 0, -28497479105, 1851629515205535]\) | \(207530301091125281552569/805586668007040\) | \(9935135576751003664971202560\) | \([2]\) | \(619315200\) | \(4.5854\) | |
346560.lc2 | 346560lc4 | \([0, 1, 0, -5400872385, -117958748165217]\) | \(1412712966892699019449/330160465517040000\) | \(4071801479920161210299842560000\) | \([2]\) | \(619315200\) | \(4.5854\) |
Rank
sage: E.rank()
The elliptic curves in class 346560lc have rank \(0\).
Complex multiplication
The elliptic curves in class 346560lc do not have complex multiplication.Modular form 346560.2.a.lc
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.