Properties

Label 203280.eh
Number of curves $4$
Conductor $203280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.eh1 203280bz3 [0, 1, 0, -723136, 236447924] [2] 1966080  
203280.eh2 203280bz2 [0, 1, 0, -45536, 3624564] [2, 2] 983040  
203280.eh3 203280bz1 [0, 1, 0, -6816, -139020] [2] 491520 \(\Gamma_0(N)\)-optimal
203280.eh4 203280bz4 [0, 1, 0, 12544, 12290100] [2] 1966080  

Rank

sage: E.rank()
 

The elliptic curves in class 203280.eh have rank \(0\).

Complex multiplication

The elliptic curves in class 203280.eh do not have complex multiplication.

Modular form 203280.2.a.eh

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.