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Properties

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

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 33810.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.be1 33810bd2 \([1, 0, 1, -11884, 497396]\) \(1577505447721/838350\) \(98631039150\) \([2]\) \(82944\) \(1.0593\)  
33810.be2 33810bd1 \([1, 0, 1, -614, 10532]\) \(-217081801/285660\) \(-33607613340\) \([2]\) \(41472\) \(0.71273\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33810.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} - 4 q^{13} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.