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Properties

Label 127050jg
Number of curves $2$
Conductor $127050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jg1")
 
E.isogeny_class()
 

Elliptic curves in class 127050jg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.jb1 127050jg1 \([1, 0, 0, -20633, -1136343]\) \(4386781853/27216\) \(6026850522000\) \([2]\) \(448000\) \(1.2903\) \(\Gamma_0(N)\)-optimal
127050.jb2 127050jg2 \([1, 0, 0, -8533, -2455243]\) \(-310288733/11573604\) \(-2562918184480500\) \([2]\) \(896000\) \(1.6369\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127050jg have rank \(0\).

Complex multiplication

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

Modular form 127050.2.a.jg

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