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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 118354g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118354.g2 | 118354g1 | \([1, -1, 0, -138152, -19136308]\) | \(6913292625/236708\) | \(9984469757093828\) | \([2]\) | \(835200\) | \(1.8419\) | \(\Gamma_0(N)\)-optimal |
118354.g1 | 118354g2 | \([1, -1, 0, -2191942, -1248535002]\) | \(27612067640625/34102\) | \(1438440558225382\) | \([2]\) | \(1670400\) | \(2.1884\) |
Rank
sage: E.rank()
The elliptic curves in class 118354g have rank \(1\).
Complex multiplication
The elliptic curves in class 118354g do not have complex multiplication.Modular form 118354.2.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 Cremona 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 Cremona labels.