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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 164730.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.n1 | 164730dk4 | \([1, 1, 0, -279613, -57014567]\) | \(100162392144121/23457780\) | \(566213783336820\) | \([2]\) | \(2359296\) | \(1.8213\) | |
164730.n2 | 164730dk3 | \([1, 1, 0, -129333, 17355537]\) | \(9912050027641/311647500\) | \(7522413034927500\) | \([2]\) | \(2359296\) | \(1.8213\) | |
164730.n3 | 164730dk2 | \([1, 1, 0, -19513, -676907]\) | \(34043726521/11696400\) | \(282322662051600\) | \([2, 2]\) | \(1179648\) | \(1.4747\) | |
164730.n4 | 164730dk1 | \([1, 1, 0, 3607, -71163]\) | \(214921799/218880\) | \(-5283231102720\) | \([2]\) | \(589824\) | \(1.1281\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.n have rank \(1\).
Complex multiplication
The elliptic curves in class 164730.n do not have complex multiplication.Modular form 164730.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.