Properties

Label 33488.q
Number of curves $2$
Conductor $33488$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33488.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33488.q1 33488z2 \([0, 0, 0, -335, -198]\) \(16241202000/9332687\) \(2389167872\) \([2]\) \(11520\) \(0.48914\)  
33488.q2 33488z1 \([0, 0, 0, -220, 1251]\) \(73598976000/336973\) \(5391568\) \([2]\) \(5760\) \(0.14257\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33488.q have rank \(0\).

Complex multiplication

The elliptic curves in class 33488.q do not have complex multiplication.

Modular form 33488.2.a.q

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