Properties

Label 158400cg
Number of curves $4$
Conductor $158400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 158400cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.h3 158400cg1 \([0, 0, 0, -3073800, 2073287000]\) \(275361373935616/148240125\) \(1729072818000000000\) \([2]\) \(4718592\) \(2.4486\) \(\Gamma_0(N)\)-optimal
158400.h2 158400cg2 \([0, 0, 0, -3618300, 1288118000]\) \(28071778927696/12404390625\) \(2314956996000000000000\) \([2, 2]\) \(9437184\) \(2.7952\)  
158400.h4 158400cg3 \([0, 0, 0, 12419700, 9595802000]\) \(283811208976796/217529296875\) \(-162384750000000000000000\) \([2]\) \(18874368\) \(3.1418\)  
158400.h1 158400cg4 \([0, 0, 0, -28368300, -57270382000]\) \(3382175663521924/59189241375\) \(44184531929472000000000\) \([2]\) \(18874368\) \(3.1418\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158400cg have rank \(1\).

Complex multiplication

The elliptic curves in class 158400cg do not have complex multiplication.

Modular form 158400.2.a.cg

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.