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Properties

Label 430.c
Number of curves $3$
Conductor $430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 430.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430.c1 430c3 \([1, 0, 0, -5626, -162894]\) \(-19693718244927649/167968750\) \(-167968750\) \([]\) \(648\) \(0.74661\)  
430.c2 430c2 \([1, 0, 0, -36, -440]\) \(-5168743489/79507000\) \(-79507000\) \([3]\) \(216\) \(0.19731\)  
430.c3 430c1 \([1, 0, 0, 4, 16]\) \(6967871/110080\) \(-110080\) \([3]\) \(72\) \(-0.35200\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 430.c have rank \(1\).

Complex multiplication

The elliptic curves in class 430.c do not have complex multiplication.

Modular form 430.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 6 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} + 2 q^{15} + q^{16} - 6 q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.