Properties

Label 127050bu
Number of curves $2$
Conductor $127050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 127050bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.k2 127050bu1 \([1, 1, 0, 41098041675, -898220963617875]\) \(2218712073897830722499107/1384711926834951880704\) \(-4791214151983699587366912000000000\) \([2]\) \(1006387200\) \(5.1518\) \(\Gamma_0(N)\)-optimal
127050.k1 127050bu2 \([1, 1, 0, -171397318325, -7327268080417875]\) \(160934676078320454012702173/86430430219822569086976\) \(299056209747381035770102128000000000\) \([2]\) \(2012774400\) \(5.4983\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127050bu have rank \(1\).

Complex multiplication

The elliptic curves in class 127050bu do not have complex multiplication.

Modular form 127050.2.a.bu

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.