Properties

Label 832j
Number of curves $2$
Conductor $832$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 832j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
832.a2 832j1 \([0, 0, 0, -172, -1328]\) \(-2146689/1664\) \(-436207616\) \([]\) \(384\) \(0.35656\) \(\Gamma_0(N)\)-optimal
832.a1 832j2 \([0, 0, 0, -13612, 670672]\) \(-1064019559329/125497034\) \(-32898294480896\) \([]\) \(2688\) \(1.3295\)  

Rank

sage: E.rank()
 

The elliptic curves in class 832j have rank \(1\).

Complex multiplication

The elliptic curves in class 832j do not have complex multiplication.

Modular form 832.2.a.j

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.