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Properties

Label 8050t
Number of curves $2$
Conductor $8050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 8050t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8050.t2 8050t1 \([1, 0, 0, 22908362, -47057366108]\) \(3403656999841015798655/4418852112356605952\) \(-1726114106389299200000000\) \([3]\) \(1088640\) \(3.3366\) \(\Gamma_0(N)\)-optimal
8050.t1 8050t2 \([1, 0, 0, -651331638, -6436892566108]\) \(-78229436189152112196207745/549794097750525813248\) \(-214763319433799145800000000\) \([]\) \(3265920\) \(3.8859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8050t have rank \(0\).

Complex multiplication

The elliptic curves in class 8050t do not have complex multiplication.

Modular form 8050.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2 q^{9} + 3 q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{16} + 3 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.