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Properties

Label 33282.x
Number of curves $2$
Conductor $33282$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 33282.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33282.x1 33282ba2 \([1, -1, 1, -996812888, -12114657249825]\) \(-23769846831649063249/3261823333284\) \(-15031374559221479789305764\) \([]\) \(17385984\) \(3.8488\)  
33282.x2 33282ba1 \([1, -1, 1, 2645572, 3699696255]\) \(444369620591/1540767744\) \(-7100279415045252071424\) \([]\) \(2483712\) \(2.8759\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33282.x have rank \(2\).

Complex multiplication

The elliptic curves in class 33282.x do not have complex multiplication.

Modular form 33282.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 5 q^{11} - 7 q^{13} - q^{14} + q^{16} - 4 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.