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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 33800.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33800.o1 | 33800a4 | \([0, 0, 0, -2378675, -1411023250]\) | \(9636491538/8125\) | \(1254970340000000000\) | \([2]\) | \(516096\) | \(2.4003\) | |
| 33800.o2 | 33800a2 | \([0, 0, 0, -181675, -11534250]\) | \(8586756/4225\) | \(326292288400000000\) | \([2, 2]\) | \(258048\) | \(2.0537\) | |
| 33800.o3 | 33800a1 | \([0, 0, 0, -97175, 11534250]\) | \(5256144/65\) | \(1254970340000000\) | \([2]\) | \(129024\) | \(1.7072\) | \(\Gamma_0(N)\)-optimal |
| 33800.o4 | 33800a3 | \([0, 0, 0, 663325, -88429250]\) | \(208974222/142805\) | \(-22057358695840000000\) | \([2]\) | \(516096\) | \(2.4003\) |
Rank
sage: E.rank()
The elliptic curves in class 33800.o have rank \(1\).
Complex multiplication
The elliptic curves in class 33800.o do not have complex multiplication.Modular form 33800.2.a.o
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.
