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SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 296450gg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.gg2 | 296450gg1 | \([1, 0, 0, -1188888, -418521608]\) | \(46585/8\) | \(31914676951128125000\) | \([]\) | \(10886400\) | \(2.4628\) | \(\Gamma_0(N)\)-optimal |
296450.gg1 | 296450gg2 | \([1, 0, 0, -27128263, 54339499017]\) | \(553463785/512\) | \(2042539324872200000000\) | \([]\) | \(32659200\) | \(3.0121\) |
Rank
sage: E.rank()
The elliptic curves in class 296450gg have rank \(0\).
Complex multiplication
The elliptic curves in class 296450gg do not have complex multiplication.Modular form 296450.2.a.gg
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.