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Properties

Label 411840.cp
Number of curves $2$
Conductor $411840$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 411840.cp have rank \(1\).

Complex multiplication

The elliptic curves in class 411840.cp do not have complex multiplication.

Modular form 411840.2.a.cp

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - q^{11} - q^{13} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 411840.cp

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
411840.cp1 411840cp1 \([0, 0, 0, -638988, 5672828912]\) \(-4076600308125723/1961812478912000\) \(-13885489002741497856000\) \([]\) \(20901888\) \(2.9279\) \(\Gamma_0(N)\)-optimal
411840.cp2 411840cp2 \([0, 0, 0, 5749812, -153005370768]\) \(4074304020054813/1962402098708480\) \(-10125563791639579679784960\) \([]\) \(62705664\) \(3.4772\)