Properties

Label 20328q
Number of curves $4$
Conductor $20328$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 20328q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20328.f4 20328q1 \([0, -1, 0, -887, -65712]\) \(-2725888/64827\) \(-1837519759152\) \([2]\) \(34560\) \(1.0340\) \(\Gamma_0(N)\)-optimal
20328.f3 20328q2 \([0, -1, 0, -30532, -2034140]\) \(6940769488/35721\) \(16200174203136\) \([2, 2]\) \(69120\) \(1.3806\)  
20328.f1 20328q3 \([0, -1, 0, -487912, -131015300]\) \(7080974546692/189\) \(342860829696\) \([2]\) \(138240\) \(1.7271\)  
20328.f2 20328q4 \([0, -1, 0, -47472, 493308]\) \(6522128932/3720087\) \(6748529710906368\) \([2]\) \(138240\) \(1.7271\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20328q have rank \(1\).

Complex multiplication

The elliptic curves in class 20328q do not have complex multiplication.

Modular form 20328.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.