Properties

Label 369600.qd
Number of curves $4$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("qd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.qd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.qd1 369600qd4 \([0, 1, 0, -4959633, 2239858863]\) \(52702650535889104/22020583921875\) \(5637269484000000000000\) \([2]\) \(23887872\) \(2.8707\)  
369600.qd2 369600qd2 \([0, 1, 0, -4275633, 3401470863]\) \(33766427105425744/9823275\) \(2514758400000000\) \([2]\) \(7962624\) \(2.3214\)  
369600.qd3 369600qd1 \([0, 1, 0, -266133, 53538363]\) \(-130287139815424/2250652635\) \(-36010442160000000\) \([2]\) \(3981312\) \(1.9748\) \(\Gamma_0(N)\)-optimal
369600.qd4 369600qd3 \([0, 1, 0, 1029867, 257334363]\) \(7549996227362816/6152409907875\) \(-98438558526000000000\) \([2]\) \(11943936\) \(2.5241\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.qd have rank \(1\).

Complex multiplication

The elliptic curves in class 369600.qd do not have complex multiplication.

Modular form 369600.2.a.qd

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.