Properties

Label 227430.a
Number of curves $2$
Conductor $227430$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("227430.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.a1 227430ex1 [1, -1, 0, -5695537680, 165445113797100] [2] 141926400 \(\Gamma_0(N)\)-optimal
227430.a2 227430ex2 [1, -1, 0, -5695310250, 165458987072586] [2] 283852800  

Rank

sage: E.rank()
 

The elliptic curves in class 227430.a have rank \(1\).

Modular form 227430.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 6q^{11} - 2q^{13} + q^{14} + q^{16} + 4q^{17} + O(q^{20}) \)

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 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.