Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("37485.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37485.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37485.bd1 37485s4 [1, -1, 0, -743535, 246949870] [2] 393216  
37485.bd2 37485s3 [1, -1, 0, -236385, -41062820] [2] 393216  
37485.bd3 37485s2 [1, -1, 0, -48960, 3431875] [2, 2] 196608  
37485.bd4 37485s1 [1, -1, 0, 6165, 311800] [2] 98304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 37485.2.a.bd

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - q^{5} - 3q^{8} - q^{10} + 6q^{13} - q^{16} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.