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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 17850.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17850.cg1 | 17850cd2 | \([1, 0, 0, -942088, -351594208]\) | \(5918043195362419129/8515734343200\) | \(133058349112500000\) | \([2]\) | \(368640\) | \(2.1882\) | |
17850.cg2 | 17850cd1 | \([1, 0, 0, -42088, -8694208]\) | \(-527690404915129/1782829440000\) | \(-27856710000000000\) | \([2]\) | \(184320\) | \(1.8417\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17850.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 17850.cg do not have complex multiplication.Modular form 17850.2.a.cg
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.