Properties

Label 41405.h
Number of curves $3$
Conductor $41405$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41405.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.h1 41405d3 \([0, -1, 1, -1087571, 457033527]\) \(-250523582464/13671875\) \(-7763837430248046875\) \([]\) \(590976\) \(2.3829\)  
41405.h2 41405d1 \([0, -1, 1, -11041, -491723]\) \(-262144/35\) \(-19875423821435\) \([]\) \(65664\) \(1.2843\) \(\Gamma_0(N)\)-optimal
41405.h3 41405d2 \([0, -1, 1, 71769, 1239006]\) \(71991296/42875\) \(-24347394181257875\) \([]\) \(196992\) \(1.8336\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41405.h have rank \(0\).

Complex multiplication

The elliptic curves in class 41405.h do not have complex multiplication.

Modular form 41405.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} - q^{5} - 2q^{9} + 3q^{11} + 2q^{12} + q^{15} + 4q^{16} - 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.