Properties

Label 101430.j
Number of curves $2$
Conductor $101430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 101430.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.j1 101430g2 \([1, -1, 0, -195117960, -183657323200]\) \(258620799050621485981803/145075171220000000000\) \(460834618109268060000000000\) \([2]\) \(40550400\) \(3.8064\)  
101430.j2 101430g1 \([1, -1, 0, -121359240, 511872654656]\) \(62228632040416581492843/382900201062400000\) \(1216291295379338035200000\) \([2]\) \(20275200\) \(3.4599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101430.j have rank \(1\).

Complex multiplication

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

Modular form 101430.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4 q^{11} + q^{16} - 4 q^{17} + O(q^{20})\) 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 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.