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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 96600.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.cd1 | 96600ck4 | \([0, 1, 0, -1656408, 819986688]\) | \(31412749404762436/7455105\) | \(119281680000000\) | \([2]\) | \(1032192\) | \(2.0797\) | |
| 96600.cd2 | 96600ck2 | \([0, 1, 0, -103908, 12686688]\) | \(31018076123344/472410225\) | \(1889640900000000\) | \([2, 2]\) | \(516096\) | \(1.7331\) | |
| 96600.cd3 | 96600ck1 | \([0, 1, 0, -12783, -253062]\) | \(924093773824/427810005\) | \(106952501250000\) | \([2]\) | \(258048\) | \(1.3866\) | \(\Gamma_0(N)\)-optimal |
| 96600.cd4 | 96600ck3 | \([0, 1, 0, -9408, 34988688]\) | \(-5756278756/33056218125\) | \(-528899490000000000\) | \([2]\) | \(1032192\) | \(2.0797\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.cd do not have complex multiplication.Modular form 96600.2.a.cd
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.
