Properties

Label 334400.br
Number of curves $2$
Conductor $334400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 334400.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334400.br1 334400br1 \([0, -1, 0, -2733, -63413]\) \(-2258403328/480491\) \(-480491000000\) \([]\) \(373248\) \(0.96288\) \(\Gamma_0(N)\)-optimal
334400.br2 334400br2 \([0, -1, 0, 19267, 365587]\) \(790939860992/517504691\) \(-517504691000000\) \([]\) \(1119744\) \(1.5122\)  

Rank

sage: E.rank()
 

The elliptic curves in class 334400.br have rank \(0\).

Complex multiplication

The elliptic curves in class 334400.br do not have complex multiplication.

Modular form 334400.2.a.br

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.