Properties

Label 430950.hc
Number of curves $2$
Conductor $430950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hc1")
 
E.isogeny_class()
 

Elliptic curves in class 430950.hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.hc1 430950hc2 \([1, 0, 0, -12497638, -17006566708]\) \(-71559517896165625/4598568\) \(-13872755880945000\) \([]\) \(14805504\) \(2.5563\)  
430950.hc2 430950hc1 \([1, 0, 0, -139513, -27985933]\) \(-99546915625/54454842\) \(-164276950911986250\) \([]\) \(4935168\) \(2.0070\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 430950.hc1.

Rank

sage: E.rank()
 

The elliptic curves in class 430950.hc have rank \(0\).

Complex multiplication

The elliptic curves in class 430950.hc do not have complex multiplication.

Modular form 430950.2.a.hc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.