Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.p1 327990p3 \([1, 0, 1, -3554684153, 81569971645598]\) \(8351005675201800382877041/395069604635949750\) \(234996614255712626284119750\) \([2]\) \(348364800\) \(4.1341\)  
327990.p2 327990p4 \([1, 0, 1, -1117886653, -13346698711402]\) \(259734139401368855237041/20937966860481050250\) \(12454390982939281967272880250\) \([2]\) \(348364800\) \(4.1341\)  
327990.p3 327990p2 \([1, 0, 1, -233785403, 1133818842098]\) \(2375679751819859057041/441134740310062500\) \(262397231239703945967562500\) \([2, 2]\) \(174182400\) \(3.7875\)  
327990.p4 327990p1 \([1, 0, 1, 29027097, 103278467098]\) \(4547226203385942959/10377808593750000\) \(-6172962572436714843750000\) \([2]\) \(87091200\) \(3.4409\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 327990.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} + q^{13} + 4q^{14} + q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.