Properties

Label 40128a
Number of curves $2$
Conductor $40128$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 40128a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40128.q2 40128a1 \([0, -1, 0, -1453, -22505]\) \(-5304438784000/497763387\) \(-31856856768\) \([]\) \(25920\) \(0.75744\) \(\Gamma_0(N)\)-optimal
40128.q1 40128a2 \([0, -1, 0, -120253, -16010609]\) \(-3004935183806464000/2037123\) \(-130375872\) \([]\) \(77760\) \(1.3067\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40128a have rank \(1\).

Complex multiplication

The elliptic curves in class 40128a do not have complex multiplication.

Modular form 40128.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} - q^{11} + q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.