Properties

Label 457776bw
Number of curves $2$
Conductor $457776$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 457776bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.bw2 457776bw1 \([0, 0, 0, -428022651, -3402909659990]\) \(591139158854005457801/1097587482427392\) \(16101761362124191159025664\) \([2]\) \(156893184\) \(3.7275\) \(\Gamma_0(N)\)-optimal
457776.bw1 457776bw2 \([0, 0, 0, -6845307771, -217990506787670]\) \(2418067440128989194388361/8359273562112\) \(122631708372043409915904\) \([2]\) \(313786368\) \(4.0741\)  

Rank

sage: E.rank()
 

The elliptic curves in class 457776bw have rank \(0\).

Complex multiplication

The elliptic curves in class 457776bw do not have complex multiplication.

Modular form 457776.2.a.bw

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 4 q^{7} + q^{11} - 6 q^{19} + O(q^{20})\) 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.