Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("io1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 127050io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.hu2 127050io1 \([1, 0, 0, 2962, 5292]\) \(2595575/1512\) \(-1674125145000\) \([]\) \(233280\) \(1.0350\) \(\Gamma_0(N)\)-optimal
127050.hu1 127050io2 \([1, 0, 0, -42413, 3553617]\) \(-7620530425/526848\) \(-583339606080000\) \([]\) \(699840\) \(1.5843\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 127050.2.a.io

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.