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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 229320.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.o1 | 229320dr2 | \([0, 0, 0, -2955603, 1955761598]\) | \(11151682683009628/40040325\) | \(10252250260761600\) | \([2]\) | \(3833856\) | \(2.2899\) | |
| 229320.o2 | 229320dr1 | \([0, 0, 0, -187383, 29634122]\) | \(11367178023472/651619215\) | \(41711470042394880\) | \([2]\) | \(1916928\) | \(1.9433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.o have rank \(2\).
Complex multiplication
The elliptic curves in class 229320.o do not have complex multiplication.Modular form 229320.2.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.
