Properties

Label 476850.b
Number of curves $2$
Conductor $476850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 476850.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.b1 476850b1 \([1, 1, 0, -7400394250, -245004103923500]\) \(118843307222596927933249/19794099600000000\) \(7465335076373006250000000000\) \([2]\) \(928972800\) \(4.3562\) \(\Gamma_0(N)\)-optimal
476850.b2 476850b2 \([1, 1, 0, -6677894250, -294748951423500]\) \(-87323024620536113533249/48975797371840020000\) \(-18471198256137611557990312500000\) \([2]\) \(1857945600\) \(4.7027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 476850.b have rank \(1\).

Complex multiplication

The elliptic curves in class 476850.b do not have complex multiplication.

Modular form 476850.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{11} - q^{12} - 4 q^{13} + 4 q^{14} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.