Properties

Label 29744.y
Number of curves $3$
Conductor $29744$
CM no
Rank $1$
Graph

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

Elliptic curves in class 29744.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29744.y1 29744z3 \([0, 1, 0, -21146181, 37420901363]\) \(-52893159101157376/11\) \(-217476706304\) \([]\) \(432000\) \(2.4723\)  
29744.y2 29744z2 \([0, 1, 0, -27941, 3246803]\) \(-122023936/161051\) \(-3184076456996864\) \([]\) \(86400\) \(1.6676\)  
29744.y3 29744z1 \([0, 1, 0, -901, -25037]\) \(-4096/11\) \(-217476706304\) \([]\) \(17280\) \(0.86289\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29744.y have rank \(1\).

Complex multiplication

The elliptic curves in class 29744.y do not have complex multiplication.

Modular form 29744.2.a.y

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

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.