Properties

Label 340032.dy
Number of curves $4$
Conductor $340032$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dy1")
 
E.isogeny_class()
 

Elliptic curves in class 340032.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340032.dy1 340032dy3 \([0, 1, 0, -441089, 112604415]\) \(36204575259448513/1527466248\) \(400416112115712\) \([4]\) \(2654208\) \(1.8821\)  
340032.dy2 340032dy2 \([0, 1, 0, -28929, 1568511]\) \(10214075575873/1806590016\) \(473586733154304\) \([2, 2]\) \(1327104\) \(1.5355\)  
340032.dy3 340032dy1 \([0, 1, 0, -8449, -278785]\) \(254478514753/21762048\) \(5704790310912\) \([2]\) \(663552\) \(1.1889\) \(\Gamma_0(N)\)-optimal
340032.dy4 340032dy4 \([0, 1, 0, 55551, 9087231]\) \(72318867421247/177381135624\) \(-46499400417017856\) \([2]\) \(2654208\) \(1.8821\)  

Rank

sage: E.rank()
 

The elliptic curves in class 340032.dy have rank \(0\).

Complex multiplication

The elliptic curves in class 340032.dy do not have complex multiplication.

Modular form 340032.2.a.dy

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{13} - 2 q^{15} + 2 q^{17} + O(q^{20})\) 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 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.