Properties

Label 327990.n
Number of curves $2$
Conductor $327990$
CM no
Rank $1$
Graph

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

Elliptic curves in class 327990.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.n1 327990n1 \([1, 0, 1, -8150149, -2926210384]\) \(100654290922421809/52033093632000\) \(30950497556090191872000\) \([2]\) \(32256000\) \(3.0076\) \(\Gamma_0(N)\)-optimal
327990.n2 327990n2 \([1, 0, 1, 30603131, -22721385808]\) \(5328847957372469711/3458851344000000\) \(-2057405443283393424000000\) \([2]\) \(64512000\) \(3.3542\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.n have rank \(1\).

Complex multiplication

The elliptic curves in class 327990.n do not have complex multiplication.

Modular form 327990.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + q^{13} - 2q^{14} - q^{15} + q^{16} + 2q^{17} - q^{18} + 6q^{19} + O(q^{20})\)  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 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.