Properties

Label 3330.i
Number of curves $2$
Conductor $3330$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3330.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.i1 3330c2 \([1, -1, 0, -5739, -165907]\) \(1062144635427/54760\) \(1077841080\) \([2]\) \(3456\) \(0.80252\)  
3330.i2 3330c1 \([1, -1, 0, -339, -2827]\) \(-219256227/59200\) \(-1165233600\) \([2]\) \(1728\) \(0.45594\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3330.i have rank \(1\).

Complex multiplication

The elliptic curves in class 3330.i do not have complex multiplication.

Modular form 3330.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{11} - 2q^{13} + q^{16} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.