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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 35280.fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.fr1 | 35280ck4 | \([0, 0, 0, -47187, 3945186]\) | \(132304644/5\) | \(439122539520\) | \([2]\) | \(73728\) | \(1.3200\) | |
35280.fr2 | 35280ck2 | \([0, 0, 0, -3087, 55566]\) | \(148176/25\) | \(548903174400\) | \([2, 2]\) | \(36864\) | \(0.97347\) | |
35280.fr3 | 35280ck1 | \([0, 0, 0, -882, -9261]\) | \(55296/5\) | \(6861289680\) | \([2]\) | \(18432\) | \(0.62690\) | \(\Gamma_0(N)\)-optimal |
35280.fr4 | 35280ck3 | \([0, 0, 0, 5733, 314874]\) | \(237276/625\) | \(-54890317440000\) | \([2]\) | \(73728\) | \(1.3200\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.fr have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.fr do not have complex multiplication.Modular form 35280.2.a.fr
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.