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Properties

Label 353202.n
Number of curves $2$
Conductor $353202$
CM no
Rank $0$
Graph

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

Elliptic curves in class 353202.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
353202.n1 353202n2 \([1, 0, 1, -82004498, -285868622056]\) \(-23769846831649063249/3261823333284\) \(-8368946267699167497156\) \([]\) \(56899584\) \(3.2244\)  
353202.n2 353202n1 \([1, 0, 1, 217642, 87331304]\) \(444369620591/1540767744\) \(-3953188490916151296\) \([]\) \(8128512\) \(2.2514\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 353202.n have rank \(0\).

Complex multiplication

The elliptic curves in class 353202.n do not have complex multiplication.

Modular form 353202.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.