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Properties

Label 365690.n
Number of curves $2$
Conductor $365690$
CM no
Rank $1$
Graph

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

Elliptic curves in class 365690.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
365690.n1 365690n2 \([1, -1, 1, -802936767, -8852366332401]\) \(-57248979119863765781565932014401/724755414877958811216956840\) \(-724755414877958811216956840\) \([]\) \(474360768\) \(3.9638\)  
365690.n2 365690n1 \([1, -1, 1, -2336967, 8297239359]\) \(-1411501283414687166603201/28919656992112640000000\) \(-28919656992112640000000\) \([7]\) \(67765824\) \(2.9908\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 365690.n have rank \(1\).

Complex multiplication

The elliptic curves in class 365690.n do not have complex multiplication.

Modular form 365690.2.a.n

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