Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 3300.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3300.o1 3300q1 \([0, 1, 0, -1013, -10572]\) \(57537462272/10673289\) \(21346578000\) \([2]\) \(2304\) \(0.70022\) \(\Gamma_0(N)\)-optimal
3300.o2 3300q2 \([0, 1, 0, 2012, -58972]\) \(28134667888/64304361\) \(-2057739552000\) \([2]\) \(4608\) \(1.0468\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3300.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + q^{11} - 4 q^{13} - 8 q^{19} + O(q^{20})\) 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.