Properties

Label 3300.b
Number of curves $4$
Conductor $3300$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3300.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3300.b1 3300e4 \([0, -1, 0, -6249908, -6011849688]\) \(6749703004355978704/5671875\) \(22687500000000\) \([2]\) \(41472\) \(2.2983\)  
3300.b2 3300e3 \([0, -1, 0, -390533, -93880938]\) \(-26348629355659264/24169921875\) \(-6042480468750000\) \([2]\) \(20736\) \(1.9517\)  
3300.b3 3300e2 \([0, -1, 0, -78908, -7829688]\) \(13584145739344/1195803675\) \(4783214700000000\) \([2]\) \(13824\) \(1.7490\)  
3300.b4 3300e1 \([0, -1, 0, 5467, -573438]\) \(72268906496/606436875\) \(-151609218750000\) \([2]\) \(6912\) \(1.4024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3300.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.