Properties

Label 187200.hj
Number of curves $4$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hj1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.hj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.hj1 187200ef3 \([0, 0, 0, -1540346700, -18008806606000]\) \(1082883335268084577352/251301565117746585\) \(93797806577068677358080000000\) \([2]\) \(165150720\) \(4.2713\)  
187200.hj2 187200ef2 \([0, 0, 0, -1441481700, -21063537376000]\) \(7099759044484031233216/577161945398025\) \(26928067724490254400000000\) \([2, 2]\) \(82575360\) \(3.9247\)  
187200.hj3 187200ef1 \([0, 0, 0, -1441453575, -21064400476000]\) \(454357982636417669333824/3003024375\) \(2189204769375000000\) \([2]\) \(41287680\) \(3.5782\) \(\Gamma_0(N)\)-optimal
187200.hj4 187200ef4 \([0, 0, 0, -1343066700, -24063029746000]\) \(-717825640026599866952/254764560814329735\) \(-95090362794826944929280000000\) \([2]\) \(165150720\) \(4.2713\)  

Rank

sage: E.rank()
 

The elliptic curves in class 187200.hj have rank \(0\).

Complex multiplication

The elliptic curves in class 187200.hj do not have complex multiplication.

Modular form 187200.2.a.hj

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} + q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.