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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 275880u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
275880.u4 | 275880u1 | \([0, -1, 0, 2380, -78780]\) | \(3286064/7695\) | \(-3489833445120\) | \([2]\) | \(491520\) | \(1.0907\) | \(\Gamma_0(N)\)-optimal |
275880.u3 | 275880u2 | \([0, -1, 0, -19400, -854148]\) | \(445138564/81225\) | \(147348523238400\) | \([2, 2]\) | \(983040\) | \(1.4373\) | |
275880.u2 | 275880u3 | \([0, -1, 0, -92000, 9977772]\) | \(23735908082/1954815\) | \(7092375585208320\) | \([2]\) | \(1966080\) | \(1.7839\) | |
275880.u1 | 275880u4 | \([0, -1, 0, -295280, -61658100]\) | \(784767874322/35625\) | \(129253090560000\) | \([2]\) | \(1966080\) | \(1.7839\) |
Rank
sage: E.rank()
The elliptic curves in class 275880u have rank \(1\).
Complex multiplication
The elliptic curves in class 275880u do not have complex multiplication.Modular form 275880.2.a.u
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.