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Properties

Label 430950b
Number of curves $2$
Conductor $430950$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 430950b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.b1 430950b1 \([1, 1, 0, -2993500, 1991237500]\) \(39335220262729/23271300\) \(1755095629401562500\) \([2]\) \(14450688\) \(2.4453\) \(\Gamma_0(N)\)-optimal
430950.b2 430950b2 \([1, 1, 0, -2444250, 2745357750]\) \(-21413157997609/30812096250\) \(-2323814117005722656250\) \([2]\) \(28901376\) \(2.7919\)  

Rank

sage: E.rank()
 

The elliptic curves in class 430950b have rank \(2\).

Complex multiplication

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

Modular form 430950.2.a.b

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