Properties

Label 29435c
Number of curves $3$
Conductor $29435$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29435c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29435.c2 29435c1 \([0, -1, 1, -1121, 16407]\) \(-262144/35\) \(-20818816235\) \([]\) \(16632\) \(0.71250\) \(\Gamma_0(N)\)-optimal
29435.c3 29435c2 \([0, -1, 1, 7289, -43304]\) \(71991296/42875\) \(-25503049887875\) \([]\) \(49896\) \(1.2618\)  
29435.c1 29435c3 \([0, -1, 1, -110451, -14743143]\) \(-250523582464/13671875\) \(-8132350091796875\) \([]\) \(149688\) \(1.8111\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29435c have rank \(0\).

Complex multiplication

The elliptic curves in class 29435c do not have complex multiplication.

Modular form 29435.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} - q^{5} + q^{7} - 2q^{9} + 3q^{11} + 2q^{12} + 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.