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Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 101430.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.g1 101430bb2 \([1, -1, 0, -860190, -306856684]\) \(281504613025066887/1354240\) \(338623649280\) \([2]\) \(1032192\) \(1.8349\)  
101430.g2 101430bb1 \([1, -1, 0, -53790, -4779244]\) \(68835304542087/150732800\) \(37690284441600\) \([2]\) \(516096\) \(1.4883\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101430.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4 q^{11} - 4 q^{13} + q^{16} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.