Properties

Label 41971a
Number of curves $3$
Conductor $41971$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 41971a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41971.a3 41971a1 \([0, 1, 1, 1473, 1452]\) \(32768/19\) \(-204805091251\) \([]\) \(35190\) \(0.85990\) \(\Gamma_0(N)\)-optimal
41971.a2 41971a2 \([0, 1, 1, -20617, 1205357]\) \(-89915392/6859\) \(-73934637941611\) \([]\) \(105570\) \(1.4092\)  
41971.a1 41971a3 \([0, 1, 1, -1699457, 852167382]\) \(-50357871050752/19\) \(-204805091251\) \([]\) \(316710\) \(1.9585\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41971a have rank \(0\).

Complex multiplication

The elliptic curves in class 41971a do not have complex multiplication.

Modular form 41971.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 2q^{4} - 3q^{5} - q^{7} + q^{9} - 3q^{11} + 4q^{12} + 4q^{13} + 6q^{15} + 4q^{16} - 3q^{17} - q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.