Properties

Label 180336bw
Number of curves $2$
Conductor $180336$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 180336bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180336.bp2 180336bw1 \([0, -1, 0, -1541, -20412]\) \(1048576/117\) \(45185529168\) \([2]\) \(245760\) \(0.77751\) \(\Gamma_0(N)\)-optimal
180336.bp1 180336bw2 \([0, -1, 0, -5876, 152988]\) \(3631696/507\) \(3132863355648\) \([2]\) \(491520\) \(1.1241\)  

Rank

sage: E.rank()
 

The elliptic curves in class 180336bw have rank \(1\).

Complex multiplication

The elliptic curves in class 180336bw do not have complex multiplication.

Modular form 180336.2.a.bw

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