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Properties

Label 123210bb
Number of curves $2$
Conductor $123210$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 123210bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123210.k2 123210bb1 \([1, -1, 0, 1558350, 2043248436]\) \(223759095911/1094104800\) \(-2046429539509200472800\) \([]\) \(7879680\) \(2.7715\) \(\Gamma_0(N)\)-optimal
123210.k1 123210bb2 \([1, -1, 0, -87337665, 314572916925]\) \(-39390416456458249/56832000000\) \(-106299399828413952000000\) \([]\) \(23639040\) \(3.3208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 123210bb have rank \(0\).

Complex multiplication

The elliptic curves in class 123210bb do not have complex multiplication.

Modular form 123210.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 3 q^{11} + 7 q^{13} + q^{14} + q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.