Properties

Label 450840.cp
Number of curves $2$
Conductor $450840$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 450840.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.cp1 450840cp1 \([0, 1, 0, -1378915, 622752410]\) \(152818608128/7605\) \(14429772812154960\) \([2]\) \(6963200\) \(2.1719\) \(\Gamma_0(N)\)-optimal
450840.cp2 450840cp2 \([0, 1, 0, -1305220, 692349968]\) \(-8100185168/2142075\) \(-65030176140111686400\) \([2]\) \(13926400\) \(2.5185\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450840.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 450840.cp do not have complex multiplication.

Modular form 450840.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4 q^{11} + q^{13} + q^{15} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.