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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 96600.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.r1 | 96600h4 | \([0, -1, 0, -2432406408, -40497400639188]\) | \(49737293673675178002921218/6641736806881023047235\) | \(212535577820192737511520000000\) | \([2]\) | \(106168320\) | \(4.3550\) | |
| 96600.r2 | 96600h2 | \([0, -1, 0, -2348371408, -43800816489188]\) | \(89516703758060574923008036/1985322833430374025\) | \(31765165334885984400000000\) | \([2, 2]\) | \(53084160\) | \(4.0085\) | |
| 96600.r3 | 96600h1 | \([0, -1, 0, -2348358908, -43801306114188]\) | \(358061097267989271289240144/176126855625\) | \(704507422500000000\) | \([2]\) | \(26542080\) | \(3.6619\) | \(\Gamma_0(N)\)-optimal |
| 96600.r4 | 96600h3 | \([0, -1, 0, -2264536408, -47072896539188]\) | \(-40133926989810174413190818/6689384645060302103835\) | \(-214060308641929667322720000000\) | \([2]\) | \(106168320\) | \(4.3550\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.r have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.r do not have complex multiplication.Modular form 96600.2.a.r
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.
