Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 101430.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.q1 101430bh4 \([1, -1, 0, -43313265, 109728974781]\) \(104778147797811105409/289854482400\) \(24859694609910770400\) \([2]\) \(7864320\) \(2.9544\)  
101430.q2 101430bh2 \([1, -1, 0, -2741265, 1669509981]\) \(26562019806177409/1343744640000\) \(115247765387341440000\) \([2, 2]\) \(3932160\) \(2.6078\)  
101430.q3 101430bh1 \([1, -1, 0, -483345, -95731875]\) \(145606291302529/37984665600\) \(3257797425994137600\) \([2]\) \(1966080\) \(2.2613\) \(\Gamma_0(N)\)-optimal
101430.q4 101430bh3 \([1, -1, 0, 1704015, 6558428925]\) \(6380108151242111/220374787500000\) \(-18900690690074287500000\) \([2]\) \(7864320\) \(2.9544\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101430.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.