↑

Properties

Label 3333.b
Number of curves $2$
Conductor $3333$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 3333.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3333.b1 3333g2 \([0, 1, 1, -54367500, -154315008862]\) \(17772225273611950625003524096/23577118962309\) \(23577118962309\) \([]\) \(160000\) \(2.7347\)  
3333.b2 3333g1 \([0, 1, 1, -109290, -4459642]\) \(144367343061390585856/75093921862509429\) \(75093921862509429\) \([5]\) \(32000\) \(1.9300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3333.b have rank \(0\).

Complex multiplication

The elliptic curves in class 3333.b do not have complex multiplication.

Modular form 3333.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - q^{13} + 4 q^{14} + q^{15} - 4 q^{16} + 3 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.