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Properties

Label 191660g
Number of curves $2$
Conductor $191660$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 191660g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191660.f2 191660g1 \([0, 1, 0, -7301, -1180585]\) \(-65536/875\) \(-574722715616000\) \([]\) \(580608\) \(1.5137\) \(\Gamma_0(N)\)-optimal
191660.f1 191660g2 \([0, 1, 0, -1102501, -445941305]\) \(-225637236736/1715\) \(-1126456522607360\) \([]\) \(1741824\) \(2.0630\)  

Rank

sage: E.rank()
 

The elliptic curves in class 191660g have rank \(1\).

Complex multiplication

The elliptic curves in class 191660g do not have complex multiplication.

Modular form 191660.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - q^{15} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.