Properties

Label 217672k
Number of curves $2$
Conductor $217672$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 217672k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
217672.r2 217672k1 \([0, -1, 0, -4788, 165476]\) \(-9826000/3703\) \(-4575660474112\) \([2]\) \(307200\) \(1.1391\) \(\Gamma_0(N)\)-optimal
217672.r1 217672k2 \([0, -1, 0, -82528, 9152220]\) \(12576878500/1127\) \(5570369272832\) \([2]\) \(614400\) \(1.4857\)  

Rank

sage: E.rank()
 

The elliptic curves in class 217672k have rank \(0\).

Complex multiplication

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

Modular form 217672.2.a.k

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} - 4q^{11} + O(q^{20})\)  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.