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Properties

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

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Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 430950dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.dk1 430950dk1 \([1, 0, 1, -14734776, -21764143802]\) \(2135227170133/832320\) \(137911514345865000000\) \([2]\) \(20127744\) \(2.8294\) \(\Gamma_0(N)\)-optimal
430950.dk2 430950dk2 \([1, 0, 1, -12537776, -28478175802]\) \(-1315451937493/1353040200\) \(-224192405508496790625000\) \([2]\) \(40255488\) \(3.1760\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 430950.2.a.dk

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