Properties

Label 33600co
Number of curves $2$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.dw2 33600co1 \([0, 1, 0, 39167, -229537]\) \(2595575/1512\) \(-3870720000000000\) \([]\) \(207360\) \(1.6805\) \(\Gamma_0(N)\)-optimal
33600.dw1 33600co2 \([0, 1, 0, -560833, -171229537]\) \(-7620530425/526848\) \(-1348730880000000000\) \([]\) \(622080\) \(2.2298\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600co have rank \(0\).

Complex multiplication

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

Modular form 33600.2.a.co

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - 6q^{11} - q^{13} - 3q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.