Properties

Label 37553.c
Number of curves $4$
Conductor $37553$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 37553.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37553.c1 37553a4 \([1, -1, 1, -200329, 34561496]\) \(82483294977/17\) \(183246660593\) \([2]\) \(105984\) \(1.5484\)  
37553.c2 37553a2 \([1, -1, 1, -12564, 538478]\) \(20346417/289\) \(3115193230081\) \([2, 2]\) \(52992\) \(1.2019\)  
37553.c3 37553a1 \([1, -1, 1, -1519, -9354]\) \(35937/17\) \(183246660593\) \([2]\) \(26496\) \(0.85529\) \(\Gamma_0(N)\)-optimal
37553.c4 37553a3 \([1, -1, 1, -1519, 1444168]\) \(-35937/83521\) \(-900290843493409\) \([2]\) \(105984\) \(1.5484\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37553.c have rank \(1\).

Complex multiplication

The elliptic curves in class 37553.c do not have complex multiplication.

Modular form 37553.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 3 q^{8} - 3 q^{9} - 2 q^{10} + 2 q^{13} - 4 q^{14} - q^{16} + q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.