Properties

Label 37485bm
Number of curves $2$
Conductor $37485$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 37485bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37485.s2 37485bm1 \([1, -1, 1, 51128428, -357315573954]\) \(172343644217341694999/742780064187984375\) \(-63705364861534434652359375\) \([2]\) \(7741440\) \(3.6339\) \(\Gamma_0(N)\)-optimal
37485.s1 37485bm2 \([1, -1, 1, -551663447, -4416998293704]\) \(216486375407331255135001/27004994294227023375\) \(2316113608242984488250078375\) \([2]\) \(15482880\) \(3.9805\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37485bm have rank \(0\).

Complex multiplication

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

Modular form 37485.2.a.bm

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.