Properties

Label 377520.hs
Number of curves $4$
Conductor $377520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 377520.hs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.hs1 377520hs3 \([0, 1, 0, -1006760, 388474260]\) \(31103978031362/195\) \(707490600960\) \([2]\) \(3932160\) \(1.8793\)  
377520.hs2 377520hs4 \([0, 1, 0, -87160, 945140]\) \(20183398562/11567205\) \(41967634958346240\) \([2]\) \(3932160\) \(1.8793\)  
377520.hs3 377520hs2 \([0, 1, 0, -62960, 6046500]\) \(15214885924/38025\) \(68980333593600\) \([2, 2]\) \(1966080\) \(1.5328\)  
377520.hs4 377520hs1 \([0, 1, 0, -2460, 165900]\) \(-3631696/24375\) \(-11054540640000\) \([2]\) \(983040\) \(1.1862\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 377520.hs have rank \(0\).

Complex multiplication

The elliptic curves in class 377520.hs do not have complex multiplication.

Modular form 377520.2.a.hs

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 4q^{7} + q^{9} - q^{13} + q^{15} - 6q^{17} + O(q^{20})\)  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.