Properties

Label 227430er
Number of curves 8
Conductor 227430
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("227430.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.ba7 227430er1 [1, -1, 0, -1616445, 791124421] [2] 4644864 \(\Gamma_0(N)\)-optimal
227430.ba6 227430er2 [1, -1, 0, -1876365, 519819925] [2, 2] 9289728  
227430.ba5 227430er3 [1, -1, 0, -4784220, -3059866544] [2] 13934592  
227430.ba8 227430er4 [1, -1, 0, 6246135, 3812681425] [2] 18579456  
227430.ba4 227430er5 [1, -1, 0, -14157585, -20139648359] [2] 18579456  
227430.ba2 227430er6 [1, -1, 0, -71323740, -231809428400] [2, 2] 27869184  
227430.ba3 227430er7 [1, -1, 0, -66125340, -267036905840] [2] 55738368  
227430.ba1 227430er8 [1, -1, 0, -1141154460, -14837352383984] [2] 55738368  

Rank

sage: E.rank()
 

The elliptic curves in class 227430er have rank \(0\).

Modular form 227430.2.a.ba

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2q^{13} - q^{14} + q^{16} + 6q^{17} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.