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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 33930.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.o1 | 33930p1 | \([1, -1, 0, -8607699, -9718060235]\) | \(96751437829777336381489/771303397130240\) | \(562280176507944960\) | \([2]\) | \(1843200\) | \(2.5781\) | \(\Gamma_0(N)\)-optimal |
| 33930.o2 | 33930p2 | \([1, -1, 0, -8423379, -10154271947]\) | \(-90668250933662417694769/8657064324137881600\) | \(-6310999892296515686400\) | \([2]\) | \(3686400\) | \(2.9246\) |
Rank
sage: E.rank()
The elliptic curves in class 33930.o have rank \(0\).
Complex multiplication
The elliptic curves in class 33930.o do not have complex multiplication.Modular form 33930.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
