Properties

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

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 96330ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.cm2 96330ct1 \([1, 1, 1, -16650, 900375]\) \(-105756712489/12476160\) \(-60220041373440\) \([2]\) \(451584\) \(1.3799\) \(\Gamma_0(N)\)-optimal
96330.cm1 96330ct2 \([1, 1, 1, -273530, 54947927]\) \(468898230633769/5540400\) \(26742452583600\) \([2]\) \(903168\) \(1.7265\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96330.2.a.ct

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