Properties

Label 254320w
Number of curves $2$
Conductor $254320$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 254320w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254320.w2 254320w1 \([0, 0, 0, -653090003, 6288242803602]\) \(63422386460383257/1535220121600\) \(745711592144937459856179200\) \([2]\) \(91914240\) \(3.9408\) \(\Gamma_0(N)\)-optimal
254320.w1 254320w2 \([0, 0, 0, -1458035923, -12275580992622]\) \(705713043507894297/274379367680000\) \(133275920661548209835868160000\) \([2]\) \(183828480\) \(4.2873\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254320w have rank \(0\).

Complex multiplication

The elliptic curves in class 254320w do not have complex multiplication.

Modular form 254320.2.a.w

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