Properties

Label 33810m
Number of curves $4$
Conductor $33810$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 33810m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.c3 33810m1 \([1, 1, 0, -10789923, -13646414067]\) \(1180838681727016392361/692428800000\) \(81463555891200000\) \([2]\) \(1474560\) \(2.5690\) \(\Gamma_0(N)\)-optimal
33810.c2 33810m2 \([1, 1, 0, -10852643, -13479817203]\) \(1201550658189465626281/28577902500000000\) \(3362161651222500000000\) \([2, 2]\) \(2949120\) \(2.9156\)  
33810.c4 33810m3 \([1, 1, 0, 1397357, -42176667203]\) \(2564821295690373719/6533572090396050000\) \(-768668222863004886450000\) \([2]\) \(5898240\) \(3.2622\)  
33810.c1 33810m4 \([1, 1, 0, -24106163, 25880486493]\) \(13167998447866683762601/5158996582031250000\) \(606950788879394531250000\) \([2]\) \(5898240\) \(3.2622\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33810.2.a.m

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.