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Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 191634p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191634.i1 191634p1 \([1, 0, 1, -404768866, 1479268784180]\) \(1543980711301828683625/694488329530785792\) \(3298891959429191130641743872\) \([2]\) \(126443520\) \(3.9756\) \(\Gamma_0(N)\)-optimal
191634.i2 191634p2 \([1, 0, 1, 1403718174, 11072930833972]\) \(64396214835842146484375/48416886126535450752\) \(-229985256125670107253921839232\) \([2]\) \(252887040\) \(4.3222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 191634p have rank \(2\).

Complex multiplication

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

Modular form 191634.2.a.p

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