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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 405042.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405042.g1 | 405042g1 | \([1, 1, 0, -326351, -71327835]\) | \(81706955619457/744505344\) | \(35025909817688064\) | \([2]\) | \(6773760\) | \(1.9968\) | \(\Gamma_0(N)\)-optimal |
405042.g2 | 405042g2 | \([1, 1, 0, -95311, -170074331]\) | \(-2035346265217/264305213568\) | \(-12434471625199713408\) | \([2]\) | \(13547520\) | \(2.3434\) |
Rank
sage: E.rank()
The elliptic curves in class 405042.g have rank \(0\).
Complex multiplication
The elliptic curves in class 405042.g do not have complex multiplication.Modular form 405042.2.a.g
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.