Properties

Label 33810t
Number of curves $4$
Conductor $33810$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33810t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.v3 33810t1 \([1, 1, 0, -6229052, -6411433776]\) \(-227196402372228188089/19338934824115200\) \(-2275206343122329164800\) \([2]\) \(2211840\) \(2.8429\) \(\Gamma_0(N)\)-optimal
33810.v2 33810t2 \([1, 1, 0, -101618332, -394321479824]\) \(986396822567235411402169/6336721794060000\) \(745508982349364940000\) \([2]\) \(4423680\) \(3.1894\)  
33810.v4 33810t3 \([1, 1, 0, 36929413, -221576739]\) \(47342661265381757089751/27397579603968000000\) \(-3223297842827231232000000\) \([2]\) \(6635520\) \(3.3922\)  
33810.v1 33810t4 \([1, 1, 0, -147718267, -1957264931]\) \(3029968325354577848895529/1753440696000000000000\) \(206290544443704000000000000\) \([2]\) \(13271040\) \(3.7387\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33810t have rank \(0\).

Complex multiplication

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

Modular form 33810.2.a.t

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.