Properties

Label 229320.dq
Number of curves $4$
Conductor $229320$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.dq1 229320dc4 \([0, 0, 0, -8573187, -9661815394]\) \(396738988420322/2985255\) \(524357102685911040\) \([2]\) \(6291456\) \(2.5755\)  
229320.dq2 229320dc2 \([0, 0, 0, -546987, -144347434]\) \(206081497444/16769025\) \(1472731368654873600\) \([2, 2]\) \(3145728\) \(2.2289\)  
229320.dq3 229320dc1 \([0, 0, 0, -114807, 12361034]\) \(7622072656/1404585\) \(30839246608584960\) \([2]\) \(1572864\) \(1.8824\) \(\Gamma_0(N)\)-optimal
229320.dq4 229320dc3 \([0, 0, 0, 564333, -656221426]\) \(113157757438/1124589375\) \(-197533016906883840000\) \([2]\) \(6291456\) \(2.5755\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320.dq have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.dq do not have complex multiplication.

Modular form 229320.2.a.dq

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.