Properties

Label 37485.bj
Number of curves $4$
Conductor $37485$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 37485.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37485.bj1 37485bs4 \([1, -1, 0, -447624, 89064765]\) \(115650783909361/27072079335\) \(2321867231967209535\) \([2]\) \(589824\) \(2.2359\)  
37485.bj2 37485bs2 \([1, -1, 0, -149949, -21134520]\) \(4347507044161/258084225\) \(22134882869541225\) \([2, 2]\) \(294912\) \(1.8893\)  
37485.bj3 37485bs1 \([1, -1, 0, -147744, -21821157]\) \(4158523459441/16065\) \(1377832733865\) \([2]\) \(147456\) \(1.5428\) \(\Gamma_0(N)\)-optimal
37485.bj4 37485bs3 \([1, -1, 0, 112446, -87415497]\) \(1833318007919/39525924375\) \(-3389985212583099375\) \([2]\) \(589824\) \(2.2359\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37485.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 37485.bj do not have complex multiplication.

Modular form 37485.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{8} + q^{10} - 4 q^{11} - 2 q^{13} - q^{16} + q^{17} - 8 q^{19} + O(q^{20})\) 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.