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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 327990g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.g4 | 327990g1 | \([1, 1, 0, -23812932, 12808365264]\) | \(2510581756496128561/1333551278592000\) | \(793227400255889644032000\) | \([2]\) | \(58060800\) | \(3.2773\) | \(\Gamma_0(N)\)-optimal |
327990.g2 | 327990g2 | \([1, 1, 0, -220001412, -1246447012464]\) | \(1979758117698975186481/17510434929000000\) | \(10415615056622179209000000\) | \([2, 2]\) | \(116121600\) | \(3.6239\) | |
327990.g3 | 327990g3 | \([1, 1, 0, -66502092, -2953451550456]\) | \(-54681655838565466801/6303365630859375000\) | \(-3749388878025033521484375000\) | \([2]\) | \(232243200\) | \(3.9704\) | |
327990.g1 | 327990g4 | \([1, 1, 0, -3512516412, -80127862879464]\) | \(8057323694463985606146481/638717154543000\) | \(379923859044937497303000\) | \([2]\) | \(232243200\) | \(3.9704\) |
Rank
sage: E.rank()
The elliptic curves in class 327990g have rank \(0\).
Complex multiplication
The elliptic curves in class 327990g do not have complex multiplication.Modular form 327990.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.