Properties

Label 191634n
Number of curves $2$
Conductor $191634$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 191634n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191634.g1 191634n1 \([1, 0, 1, -168812, 2864810]\) \(7719308351835137/4415243157504\) \(304302973658333184\) \([2]\) \(2856960\) \(2.0445\) \(\Gamma_0(N)\)-optimal
191634.g2 191634n2 \([1, 0, 1, 670868, 23017130]\) \(484489425895814143/283680450809856\) \(-19551540350266085376\) \([2]\) \(5713920\) \(2.3910\)  

Rank

sage: E.rank()
 

The elliptic curves in class 191634n have rank \(0\).

Complex multiplication

The elliptic curves in class 191634n do not have complex multiplication.

Modular form 191634.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + 2 q^{10} + 4 q^{11} + q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} + 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.