Properties

Label 63210br
Number of curves $2$
Conductor $63210$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 63210br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63210.bs1 63210br1 \([1, 1, 1, -9360, -325263]\) \(770842973809/66873600\) \(7867612166400\) \([2]\) \(184320\) \(1.2152\) \(\Gamma_0(N)\)-optimal
63210.bs2 63210br2 \([1, 1, 1, 10240, -1485583]\) \(1009328859791/8734528080\) \(-1027608494083920\) \([2]\) \(368640\) \(1.5618\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63210br have rank \(0\).

Complex multiplication

The elliptic curves in class 63210br do not have complex multiplication.

Modular form 63210.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + 6 q^{13} - q^{15} + q^{16} + 4 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.