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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 38720.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.p1 | 38720dn3 | \([0, 1, 0, -20005, -1095525]\) | \(488095744/125\) | \(226759808000\) | \([2]\) | \(69120\) | \(1.1649\) | |
| 38720.p2 | 38720dn4 | \([0, 1, 0, -17585, -1368017]\) | \(-20720464/15625\) | \(-453519616000000\) | \([2]\) | \(138240\) | \(1.5115\) | |
| 38720.p3 | 38720dn1 | \([0, 1, 0, -645, 4123]\) | \(16384/5\) | \(9070392320\) | \([2]\) | \(23040\) | \(0.61557\) | \(\Gamma_0(N)\)-optimal |
| 38720.p4 | 38720dn2 | \([0, 1, 0, 1775, 29775]\) | \(21296/25\) | \(-725631385600\) | \([2]\) | \(46080\) | \(0.96214\) |
Rank
sage: E.rank()
The elliptic curves in class 38720.p have rank \(0\).
Complex multiplication
The elliptic curves in class 38720.p do not have complex multiplication.Modular form 38720.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
