Properties

Label 41280cd
Number of curves $2$
Conductor $41280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 41280cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41280.e1 41280cd1 \([0, -1, 0, -1281, 14625]\) \(3550014724/725625\) \(47554560000\) \([2]\) \(36864\) \(0.76428\) \(\Gamma_0(N)\)-optimal
41280.e2 41280cd2 \([0, -1, 0, 2719, 84225]\) \(16954370638/33698025\) \(-4416867532800\) \([2]\) \(73728\) \(1.1109\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41280cd have rank \(1\).

Complex multiplication

The elliptic curves in class 41280cd do not have complex multiplication.

Modular form 41280.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - 4 q^{11} + 6 q^{13} + q^{15} + 2 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.