Properties

Label 204624y
Number of curves $6$
Conductor $204624$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 204624y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
204624.bu5 204624y1 \([0, 0, 0, -5532051, -5362105966]\) \(-53297461115137/4513839183\) \(-1585702820019073609728\) \([2]\) \(9437184\) \(2.8129\) \(\Gamma_0(N)\)-optimal
204624.bu4 204624y2 \([0, 0, 0, -90239331, -329943461470]\) \(231331938231569617/1472026689\) \(517120078331917799424\) \([2, 2]\) \(18874368\) \(3.1595\)  
204624.bu3 204624y3 \([0, 0, 0, -91968051, -316644418510]\) \(244883173420511137/18418027974129\) \(6470216973559941872062464\) \([2, 2]\) \(37748736\) \(3.5061\)  
204624.bu1 204624y4 \([0, 0, 0, -1443827091, -21116449256686]\) \(947531277805646290177/38367\) \(13478251579011072\) \([2]\) \(37748736\) \(3.5061\)  
204624.bu2 204624y5 \([0, 0, 0, -299661411, 1623086947874]\) \(8471112631466271697/1662662681263647\) \(584090127169299994637463552\) \([2]\) \(75497472\) \(3.8526\)  
204624.bu6 204624y6 \([0, 0, 0, 88065789, -1405237035454]\) \(215015459663151503/2552757445339983\) \(-896778665741024739802902528\) \([2]\) \(75497472\) \(3.8526\)  

Rank

sage: E.rank()
 

The elliptic curves in class 204624y have rank \(0\).

Complex multiplication

The elliptic curves in class 204624y do not have complex multiplication.

Modular form 204624.2.a.y

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 4 q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.