Properties

Label 115920.p
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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

Elliptic curves in class 115920.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.p1 115920s4 \([0, 0, 0, -325083, -66919718]\) \(5089545532199524/353759765625\) \(264080250000000000\) \([2]\) \(1179648\) \(2.0908\)  
115920.p2 115920s2 \([0, 0, 0, -64263, 5014438]\) \(157267580823376/32806265625\) \(6122436516000000\) \([2, 2]\) \(589824\) \(1.7442\)  
115920.p3 115920s1 \([0, 0, 0, -60618, 5744167]\) \(2111937254864896/132040125\) \(1540116018000\) \([2]\) \(294912\) \(1.3976\) \(\Gamma_0(N)\)-optimal
115920.p4 115920s3 \([0, 0, 0, 138237, 30245938]\) \(391353415004156/755885521125\) \(-564265517977728000\) \([2]\) \(1179648\) \(2.0908\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.p have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.p do not have complex multiplication.

Modular form 115920.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.