Properties

Label 101430bg
Number of curves $4$
Conductor $101430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 101430bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.v4 101430bg1 \([1, -1, 0, -503190, 411463156]\) \(-164287467238609/757170892800\) \(-64939610409562828800\) \([2]\) \(3538944\) \(2.4864\) \(\Gamma_0(N)\)-optimal
101430.v3 101430bg2 \([1, -1, 0, -11933910, 15845221300]\) \(2191574502231419089/4115217960000\) \(352946281498733160000\) \([2, 2]\) \(7077888\) \(2.8330\)  
101430.v2 101430bg3 \([1, -1, 0, -15902910, 4401006700]\) \(5186062692284555089/2903809817953800\) \(249048504207613583209800\) \([2]\) \(14155776\) \(3.1795\)  
101430.v1 101430bg4 \([1, -1, 0, -190856430, 1014912788476]\) \(8964546681033941529169/31696875000\) \(2718518016571875000\) \([2]\) \(14155776\) \(3.1795\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430bg have rank \(0\).

Complex multiplication

The elliptic curves in class 101430bg do not have complex multiplication.

Modular form 101430.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 2 q^{13} + q^{16} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.