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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 490098.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490098.o1 | 490098o1 | \([1, 0, 1, -4975, 134306]\) | \(115714886617/320064\) | \(37655209536\) | \([2]\) | \(552960\) | \(0.90215\) | \(\Gamma_0(N)\)-optimal |
490098.o2 | 490098o2 | \([1, 0, 1, -3015, 241714]\) | \(-25750777177/200080008\) | \(-23539212861192\) | \([2]\) | \(1105920\) | \(1.2487\) |
Rank
sage: E.rank()
The elliptic curves in class 490098.o have rank \(0\).
Complex multiplication
The elliptic curves in class 490098.o do not have complex multiplication.Modular form 490098.2.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.