Properties

Label 58835a
Number of curves $3$
Conductor $58835$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 58835a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58835.f2 58835a1 \([0, -1, 1, -2241, 46056]\) \(-262144/35\) \(-166253648435\) \([]\) \(43200\) \(0.88564\) \(\Gamma_0(N)\)-optimal
58835.f3 58835a2 \([0, -1, 1, 14569, -120363]\) \(71991296/42875\) \(-203660719332875\) \([]\) \(129600\) \(1.4349\)  
58835.f1 58835a3 \([0, -1, 1, -220771, -41693174]\) \(-250523582464/13671875\) \(-64942831419921875\) \([]\) \(388800\) \(1.9842\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58835a have rank \(1\).

Complex multiplication

The elliptic curves in class 58835a do not have complex multiplication.

Modular form 58835.2.a.a

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