Properties

Label 327990.g
Number of curves $4$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.g1 327990g4 \([1, 1, 0, -3512516412, -80127862879464]\) \(8057323694463985606146481/638717154543000\) \(379923859044937497303000\) \([2]\) \(232243200\) \(3.9704\)  
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.g4 327990g1 \([1, 1, 0, -23812932, 12808365264]\) \(2510581756496128561/1333551278592000\) \(793227400255889644032000\) \([2]\) \(58060800\) \(3.2773\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327990.g have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.g do not have complex multiplication.

Modular form 327990.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - q^{13} - q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.