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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2520.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2520.j1 | 2520r3 | \([0, 0, 0, -15627, -707866]\) | \(282678688658/18600435\) | \(27770300651520\) | \([2]\) | \(6144\) | \(1.3292\) | |
2520.j2 | 2520r2 | \([0, 0, 0, -3027, 50654]\) | \(4108974916/893025\) | \(666639590400\) | \([2, 2]\) | \(3072\) | \(0.98263\) | |
2520.j3 | 2520r1 | \([0, 0, 0, -2847, 58466]\) | \(13674725584/945\) | \(176359680\) | \([4]\) | \(1536\) | \(0.63606\) | \(\Gamma_0(N)\)-optimal |
2520.j4 | 2520r4 | \([0, 0, 0, 6693, 309206]\) | \(22208984782/40516875\) | \(-60491370240000\) | \([2]\) | \(6144\) | \(1.3292\) |
Rank
sage: E.rank()
The elliptic curves in class 2520.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.j do not have complex multiplication.Modular form 2520.2.a.j
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.