Properties

Label 217672.j
Number of curves $2$
Conductor $217672$
CM no
Rank $1$
Graph

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

Elliptic curves in class 217672.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
217672.j1 217672e2 \([0, 0, 0, -165451, 25902630]\) \(50668941906/1127\) \(11140738545664\) \([2]\) \(552960\) \(1.6184\)  
217672.j2 217672e1 \([0, 0, 0, -9971, 435006]\) \(-22180932/3703\) \(-18302641896448\) \([2]\) \(276480\) \(1.2718\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 217672.j have rank \(1\).

Complex multiplication

The elliptic curves in class 217672.j do not have complex multiplication.

Modular form 217672.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 3 q^{9} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.