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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 127050k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.d2 127050k1 \([1, 1, 0, 225300, -639126000]\) \(604175/84672\) \(-177247999726875000000\) \([]\) \(5702400\) \(2.5647\) \(\Gamma_0(N)\)-optimal
127050.d1 127050k2 \([1, 1, 0, -49687200, -134853838500]\) \(-6480608299825/1411788\) \(-2955364217668242187500\) \([]\) \(17107200\) \(3.1140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127050k have rank \(2\).

Complex multiplication

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

Modular form 127050.2.a.k

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