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Properties

Label 430950.s
Number of curves $2$
Conductor $430950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 430950.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.s1 430950s2 \([1, 1, 0, -640500, -192600000]\) \(846509996114173/24354723600\) \(836051996081250000\) \([2]\) \(9732096\) \(2.2171\) \(\Gamma_0(N)\)-optimal*
430950.s2 430950s1 \([1, 1, 0, 9500, -9950000]\) \(2761677827/1248480000\) \(-42857977500000000\) \([2]\) \(4866048\) \(1.8705\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 430950.s1.

Rank

sage: E.rank()
 

The elliptic curves in class 430950.s have rank \(1\).

Complex multiplication

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

Modular form 430950.2.a.s

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.