Properties

Label 356048cw
Number of curves $2$
Conductor $356048$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 356048cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
356048.cw2 356048cw1 \([0, -1, 0, 1106196, -475082080]\) \(24226243449392/29774625727\) \(-183983893231267241728\) \([2]\) \(9461760\) \(2.5746\) \(\Gamma_0(N)\)-optimal
356048.cw1 356048cw2 \([0, -1, 0, -6586984, -4561699296]\) \(1278763167594532/375974556419\) \(9292914480955397540864\) \([2]\) \(18923520\) \(2.9211\)  

Rank

sage: E.rank()
 

The elliptic curves in class 356048cw have rank \(0\).

Complex multiplication

The elliptic curves in class 356048cw do not have complex multiplication.

Modular form 356048.2.a.cw

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