Properties

Label 457776fw
Number of curves $2$
Conductor $457776$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 457776fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
457776.fw1 457776fw1 [0, 0, 0, -8157603, -8962245470] [2] 21233664 \(\Gamma_0(N)\)-optimal
457776.fw2 457776fw2 [0, 0, 0, -6492963, -12725996510] [2] 42467328  

Rank

sage: E.rank()
 

The elliptic curves in class 457776fw have rank \(1\).

Complex multiplication

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

Modular form 457776.2.a.fw

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

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.