Properties

Label 76230.ek
Number of curves 4
Conductor 76230
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76230.ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.ek1 76230en4 [1, -1, 1, -28440347, -56716844929] [2] 9953280  
76230.ek2 76230en2 [1, -1, 1, -3894287, 2932642199] [2] 3317760  
76230.ek3 76230en1 [1, -1, 1, -61007, 112881431] [2] 1658880 \(\Gamma_0(N)\)-optimal
76230.ek4 76230en3 [1, -1, 1, 548833, -3040479241] [2] 4976640  

Rank

sage: E.rank()
 

The elliptic curves in class 76230.ek have rank \(1\).

Modular form 76230.2.a.ek

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 4q^{13} - q^{14} + q^{16} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.