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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 189618.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.n1 | 189618x4 | \([1, 0, 1, -237317747, -1407179633650]\) | \(306234591284035366263793/1727485056\) | \(8338240415666304\) | \([2]\) | \(24772608\) | \(3.1247\) | |
189618.n2 | 189618x2 | \([1, 0, 1, -14832627, -21987276530]\) | \(74768347616680342513/5615307472896\) | \(27104016647941668864\) | \([2, 2]\) | \(12386304\) | \(2.7782\) | |
189618.n3 | 189618x3 | \([1, 0, 1, -13859187, -24997542386]\) | \(-60992553706117024753/20624795251201152\) | \(-99551947341654981283968\) | \([2]\) | \(24772608\) | \(3.1247\) | |
189618.n4 | 189618x1 | \([1, 0, 1, -988147, -295745266]\) | \(22106889268753393/4969545596928\) | \(23987047413162442752\) | \([2]\) | \(6193152\) | \(2.4316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 189618.n have rank \(0\).
Complex multiplication
The elliptic curves in class 189618.n do not have complex multiplication.Modular form 189618.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.