Properties

Label 3300.q
Number of curves $2$
Conductor $3300$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3300.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3300.q1 3300k2 \([0, 1, 0, -9908, -382812]\) \(26894628304/9075\) \(36300000000\) \([2]\) \(4608\) \(0.99839\)  
3300.q2 3300k1 \([0, 1, 0, -533, -7812]\) \(-67108864/61875\) \(-15468750000\) \([2]\) \(2304\) \(0.65181\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3300.q have rank \(1\).

Complex multiplication

The elliptic curves in class 3300.q do not have complex multiplication.

Modular form 3300.2.a.q

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