Properties

Label 29645.e
Number of curves $2$
Conductor $29645$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29645.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.e1 29645n2 \([1, 1, 1, -12797870, 1798487032]\) \(835630707059/478515625\) \(132745109443598544921875\) \([2]\) \(2534400\) \(3.1266\)  
29645.e2 29645n1 \([1, 1, 1, 3180785, 226187380]\) \(12829337821/7503125\) \(-2081443316075625184375\) \([2]\) \(1267200\) \(2.7800\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29645.e have rank \(1\).

Complex multiplication

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

Modular form 29645.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2q^{3} - q^{4} + q^{5} - 2q^{6} + 3q^{8} + q^{9} - q^{10} - 2q^{12} + 2q^{13} + 2q^{15} - q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  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.