Properties

Label 216384n
Number of curves $2$
Conductor $216384$
CM no
Rank $1$
Graph

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

Elliptic curves in class 216384n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.fq2 216384n1 \([0, 1, 0, 1045791, 951656607]\) \(4101378352343/15049939968\) \(-464154889367121297408\) \([2]\) \(8847360\) \(2.6484\) \(\Gamma_0(N)\)-optimal
216384.fq1 216384n2 \([0, 1, 0, -10494689, 11428104351]\) \(4144806984356137/568114785504\) \(17521216428378710605824\) \([2]\) \(17694720\) \(2.9950\)  

Rank

sage: E.rank()
 

The elliptic curves in class 216384n have rank \(1\).

Complex multiplication

The elliptic curves in class 216384n do not have complex multiplication.

Modular form 216384.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} + 4 q^{13} - 2 q^{15} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.