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Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 430950w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.w2 430950w1 \([1, 1, 0, -260526685, 859043402365]\) \(16206164115169540524745/6736014906011025408\) \(812836434311704288464076800\) \([]\) \(185068800\) \(3.8607\) \(\Gamma_0(N)\)-optimal
430950.w1 430950w2 \([1, 1, 0, -9842484460, -375814911055280]\) \(873851835888094527083289145/83719665273003835392\) \(10102470845418059242615603200\) \([]\) \(555206400\) \(4.4100\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 430950.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.