Properties

Label 29645.a
Number of curves $2$
Conductor $29645$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29645.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.a1 29645b2 \([1, -1, 1, -3268, 69556]\) \(24642171/1225\) \(191823753275\) \([2]\) \(27648\) \(0.92394\)  
29645.a2 29645b1 \([1, -1, 1, -573, -3748]\) \(132651/35\) \(5480678665\) \([2]\) \(13824\) \(0.57736\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29645.a have rank \(2\).

Complex multiplication

The elliptic curves in class 29645.a do not have complex multiplication.

Modular form 29645.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3q^{8} - 3q^{9} + q^{10} - 4q^{13} - q^{16} + 3q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.