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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 158025.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158025.n1 | 158025g4 | \([1, 0, 0, -299538, -62349183]\) | \(1616855892553/22851963\) | \(42007978046671875\) | \([2]\) | \(1474560\) | \(1.9945\) | |
158025.n2 | 158025g2 | \([1, 0, 0, -36163, 1124192]\) | \(2845178713/1347921\) | \(2477836839515625\) | \([2, 2]\) | \(737280\) | \(1.6479\) | |
158025.n3 | 158025g1 | \([1, 0, 0, -30038, 2000067]\) | \(1630532233/1161\) | \(2134226390625\) | \([2]\) | \(368640\) | \(1.3014\) | \(\Gamma_0(N)\)-optimal |
158025.n4 | 158025g3 | \([1, 0, 0, 129212, 8566067]\) | \(129784785047/92307627\) | \(-169685937639421875\) | \([2]\) | \(1474560\) | \(1.9945\) |
Rank
sage: E.rank()
The elliptic curves in class 158025.n have rank \(2\).
Complex multiplication
The elliptic curves in class 158025.n do not have complex multiplication.Modular form 158025.2.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.