Properties

Label 33620a
Number of curves $4$
Conductor $33620$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 33620a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33620.a3 33620a1 \([0, -1, 0, -2241, 28826]\) \(16384/5\) \(380008339280\) \([2]\) \(34560\) \(0.92684\) \(\Gamma_0(N)\)-optimal
33620.a4 33620a2 \([0, -1, 0, 6164, 186840]\) \(21296/25\) \(-30400667142400\) \([2]\) \(69120\) \(1.2734\)  
33620.a1 33620a3 \([0, -1, 0, -69481, -7024650]\) \(488095744/125\) \(9500208482000\) \([2]\) \(103680\) \(1.4761\)  
33620.a2 33620a4 \([0, -1, 0, -61076, -8796424]\) \(-20720464/15625\) \(-19000416964000000\) \([2]\) \(207360\) \(1.8227\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33620a have rank \(0\).

Complex multiplication

The elliptic curves in class 33620a do not have complex multiplication.

Modular form 33620.2.a.a

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} - 2 q^{7} + q^{9} - 2 q^{13} - 2 q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.