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Properties

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

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

Elliptic curves in class 63210b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63210.b2 63210b1 \([1, 1, 0, -1838, -21132]\) \(5841725401/1857600\) \(218544782400\) \([2]\) \(103680\) \(0.87969\) \(\Gamma_0(N)\)-optimal
63210.b1 63210b2 \([1, 1, 0, -11638, 462988]\) \(1481933914201/53916840\) \(6343262309160\) \([2]\) \(207360\) \(1.2263\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 63210.2.a.b

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