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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 4046.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4046.o1 | 4046o1 | \([1, -1, 1, -760, 7803]\) | \(9869198625/614656\) | \(3019804928\) | \([2]\) | \(2048\) | \(0.57046\) | \(\Gamma_0(N)\)-optimal |
4046.o2 | 4046o2 | \([1, -1, 1, 600, 31739]\) | \(4869777375/92236816\) | \(-453159477008\) | \([2]\) | \(4096\) | \(0.91704\) |
Rank
sage: E.rank()
The elliptic curves in class 4046.o have rank \(1\).
Complex multiplication
The elliptic curves in class 4046.o do not have complex multiplication.Modular form 4046.2.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.