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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 27584.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.o1 | 27584w2 | \([0, 0, 0, -2156, 24144]\) | \(4227952113/1486088\) | \(389569052672\) | \([2]\) | \(20736\) | \(0.92534\) | |
27584.o2 | 27584w1 | \([0, 0, 0, 404, 2640]\) | \(27818127/27584\) | \(-7230980096\) | \([2]\) | \(10368\) | \(0.57876\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27584.o have rank \(1\).
Complex multiplication
The elliptic curves in class 27584.o do not have complex multiplication.Modular form 27584.2.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.