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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 27200.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27200.o1 | 27200n1 | \([0, 1, 0, -433, 1263]\) | \(35152/17\) | \(4352000000\) | \([2]\) | \(16384\) | \(0.54309\) | \(\Gamma_0(N)\)-optimal |
27200.o2 | 27200n2 | \([0, 1, 0, 1567, 11263]\) | \(415292/289\) | \(-295936000000\) | \([2]\) | \(32768\) | \(0.88966\) |
Rank
sage: E.rank()
The elliptic curves in class 27200.o have rank \(1\).
Complex multiplication
The elliptic curves in class 27200.o do not have complex multiplication.Modular form 27200.2.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.