Properties

Label 3450.n
Number of curves $2$
Conductor $3450$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 3450.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.n1 3450p2 \([1, 1, 1, -13007513, -18274618969]\) \(-24923353462910020825/341398360424448\) \(-3333968363520000000000\) \([]\) \(336960\) \(2.9366\)  
3450.n2 3450p1 \([1, 1, 1, 576862, -125893969]\) \(2173899265153175/1961845235712\) \(-19158644880000000000\) \([]\) \(112320\) \(2.3873\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3450.n have rank \(0\).

Complex multiplication

The elliptic curves in class 3450.n do not have complex multiplication.

Modular form 3450.2.a.n

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.