Properties

Label 129600bh
Number of curves $4$
Conductor $129600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 129600bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129600.cy3 129600bh1 \([0, 0, 0, -7500, 262000]\) \(-140625/8\) \(-2654208000000\) \([]\) \(165888\) \(1.1409\) \(\Gamma_0(N)\)-optimal
129600.cy4 129600bh2 \([0, 0, 0, 40500, 486000]\) \(3375/2\) \(-4353564672000000\) \([]\) \(497664\) \(1.6902\)  
129600.cy2 129600bh3 \([0, 0, 0, -151500, -46106000]\) \(-1159088625/2097152\) \(-695784701952000000\) \([]\) \(1161216\) \(2.1138\)  
129600.cy1 129600bh4 \([0, 0, 0, -15511500, -23514138000]\) \(-189613868625/128\) \(-278628139008000000\) \([]\) \(3483648\) \(2.6631\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129600bh have rank \(1\).

Complex multiplication

The elliptic curves in class 129600bh do not have complex multiplication.

Modular form 129600.2.a.bh

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + 3 q^{11} + 2 q^{13} + 3 q^{17} + q^{19} + O(q^{20})\) Copy content 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.