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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 46090.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46090.o1 | 46090h2 | \([1, -1, 1, -66763, -6622969]\) | \(32909792509566038529/265536012500\) | \(265536012500\) | \([2]\) | \(136320\) | \(1.3636\) | |
46090.o2 | 46090h1 | \([1, -1, 1, -4263, -97969]\) | \(8565923637038529/720156250000\) | \(720156250000\) | \([2]\) | \(68160\) | \(1.0170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46090.o have rank \(1\).
Complex multiplication
The elliptic curves in class 46090.o do not have complex multiplication.Modular form 46090.2.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.