Properties

Label 33930l
Number of curves $4$
Conductor $33930$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 33930l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33930.a4 33930l1 \([1, -1, 0, 310635, -114410075]\) \(4547226203385942959/10377808593750000\) \(-7565422464843750000\) \([2]\) \(829440\) \(2.3066\) \(\Gamma_0(N)\)-optimal
33930.a3 33930l2 \([1, -1, 0, -2501865, -1254597575]\) \(2375679751819859057041/441134740310062500\) \(321587225686035562500\) \([2, 2]\) \(1658880\) \(2.6532\)  
33930.a2 33930l3 \([1, -1, 0, -11963115, 14778436675]\) \(259734139401368855237041/20937966860481050250\) \(15263777841290685632250\) \([2]\) \(3317760\) \(2.9997\)  
33930.a1 33930l4 \([1, -1, 0, -38040615, -90293381825]\) \(8351005675201800382877041/395069604635949750\) \(288005741779607367750\) \([2]\) \(3317760\) \(2.9997\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33930l have rank \(0\).

Complex multiplication

The elliptic curves in class 33930l do not have complex multiplication.

Modular form 33930.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 4 q^{7} - q^{8} + q^{10} + 4 q^{11} + q^{13} + 4 q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.