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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 720.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 720.b1 | 720f4 | \([0, 0, 0, -3483, 20682]\) | \(57960603/31250\) | \(2519424000000\) | \([2]\) | \(1152\) | \(1.0707\) | |
| 720.b2 | 720f2 | \([0, 0, 0, -2043, -35542]\) | \(8527173507/200\) | \(22118400\) | \([2]\) | \(384\) | \(0.52136\) | |
| 720.b3 | 720f1 | \([0, 0, 0, -123, -598]\) | \(-1860867/320\) | \(-35389440\) | \([2]\) | \(192\) | \(0.17479\) | \(\Gamma_0(N)\)-optimal |
| 720.b4 | 720f3 | \([0, 0, 0, 837, 2538]\) | \(804357/500\) | \(-40310784000\) | \([2]\) | \(576\) | \(0.72409\) |
Rank
sage: E.rank()
The elliptic curves in class 720.b have rank \(0\).
Complex multiplication
The elliptic curves in class 720.b do not have complex multiplication.Modular form 720.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
