Properties

Label 33600.w
Number of curves $2$
Conductor $33600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 33600.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.w1 33600fl1 \([0, -1, 0, -272833, -54466463]\) \(4386781853/27216\) \(13934592000000000\) \([2]\) \(307200\) \(1.9358\) \(\Gamma_0(N)\)-optimal
33600.w2 33600fl2 \([0, -1, 0, -112833, -117986463]\) \(-310288733/11573604\) \(-5925685248000000000\) \([2]\) \(614400\) \(2.2824\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600.w have rank \(1\).

Complex multiplication

The elliptic curves in class 33600.w do not have complex multiplication.

Modular form 33600.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 2 q^{11} - 2 q^{13} + 8 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.