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Properties

Label 3366.h
Number of curves $2$
Conductor $3366$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 3366.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3366.h1 3366a2 \([1, -1, 0, -4902, 133334]\) \(661914925875/4114\) \(80975862\) \([2]\) \(3840\) \(0.70374\)  
3366.h2 3366a1 \([1, -1, 0, -312, 2060]\) \(170953875/12716\) \(250289028\) \([2]\) \(1920\) \(0.35717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3366.h have rank \(1\).

Complex multiplication

The elliptic curves in class 3366.h do not have complex multiplication.

Modular form 3366.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} - q^{11} + 4 q^{13} - 4 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) 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.