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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 63480.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63480.n1 | 63480p6 | \([0, 1, 0, -1692976, 847296224]\) | \(1770025017602/75\) | \(22738312550400\) | \([2]\) | \(811008\) | \(2.0477\) | |
| 63480.n2 | 63480p4 | \([0, 1, 0, -105976, 13169024]\) | \(868327204/5625\) | \(852686720640000\) | \([2, 2]\) | \(405504\) | \(1.7012\) | |
| 63480.n3 | 63480p5 | \([0, 1, 0, -42496, 28861280]\) | \(-27995042/1171875\) | \(-355286133600000000\) | \([2]\) | \(811008\) | \(2.0477\) | |
| 63480.n4 | 63480p2 | \([0, 1, 0, -10756, -85600]\) | \(3631696/2025\) | \(76741804857600\) | \([2, 2]\) | \(202752\) | \(1.3546\) | |
| 63480.n5 | 63480p1 | \([0, 1, 0, -8111, -283446]\) | \(24918016/45\) | \(106585840080\) | \([2]\) | \(101376\) | \(1.0080\) | \(\Gamma_0(N)\)-optimal |
| 63480.n6 | 63480p3 | \([0, 1, 0, 42144, -635760]\) | \(54607676/32805\) | \(-4972868954772480\) | \([2]\) | \(405504\) | \(1.7012\) |
Rank
sage: E.rank()
The elliptic curves in class 63480.n have rank \(0\).
Complex multiplication
The elliptic curves in class 63480.n do not have complex multiplication.Modular form 63480.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
