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Properties

Label 96330.g
Number of curves $2$
Conductor $96330$
CM no
Rank $0$
Graph

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

Elliptic curves in class 96330.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.g1 96330j2 \([1, 1, 0, -1897873, 1005559027]\) \(156626555801245921/19006650\) \(91741469279850\) \([2]\) \(1720320\) \(2.0988\)  
96330.g2 96330j1 \([1, 1, 0, -118303, 15762193]\) \(-37936442980801/421347420\) \(-2033763518982780\) \([2]\) \(860160\) \(1.7523\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 96330.g have rank \(0\).

Complex multiplication

The elliptic curves in class 96330.g do not have complex multiplication.

Modular form 96330.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} + 2 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.