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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8400.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.o1 | 8400bx2 | \([0, -1, 0, -1708, 24412]\) | \(1102736/147\) | \(73500000000\) | \([2]\) | \(7680\) | \(0.81273\) | |
8400.o2 | 8400bx1 | \([0, -1, 0, 167, 1912]\) | \(16384/63\) | \(-1968750000\) | \([2]\) | \(3840\) | \(0.46616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8400.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8400.o do not have complex multiplication.Modular form 8400.2.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.