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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 226576.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226576.o1 | 226576k2 | \([0, 1, 0, -6348848, 736981972]\) | \(2433138625/1387778\) | \(16142162494341757411328\) | \([2]\) | \(10616832\) | \(2.9511\) | |
226576.o2 | 226576k1 | \([0, 1, 0, -4083088, -3162844140]\) | \(647214625/3332\) | \(38756692663485612032\) | \([2]\) | \(5308416\) | \(2.6045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 226576.o have rank \(1\).
Complex multiplication
The elliptic curves in class 226576.o do not have complex multiplication.Modular form 226576.2.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.