Properties

Label 33810.e
Number of curves $2$
Conductor $33810$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 33810.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.e1 33810h2 \([1, 1, 0, -134488, 18927448]\) \(5490138280852426201/2760\) \(135240\) \([]\) \(95904\) \(1.2203\)  
33810.e2 33810h1 \([1, 1, 0, -1663, 25243]\) \(10389923853001/82127250\) \(4024235250\) \([]\) \(31968\) \(0.67097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33810.e have rank \(1\).

Complex multiplication

The elliptic curves in class 33810.e do not have complex multiplication.

Modular form 33810.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} - 5 q^{13} + q^{15} + q^{16} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.