Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("227430.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.g1 227430ge2 [1, -1, 0, -213960, 38058566] [2] 1658880  
227430.g2 227430ge1 [1, -1, 0, -8190, 1061120] [2] 829440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 227430.g have rank \(2\).

Modular form 227430.2.a.g

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

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.