Properties

Label 2601.i
Number of curves $2$
Conductor $2601$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2601.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2601.i1 2601i1 [1, -1, 0, -207, -752] [2] 768 \(\Gamma_0(N)\)-optimal
2601.i2 2601i2 [1, -1, 0, 558, -5495] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 2601.i have rank \(0\).

Complex multiplication

The elliptic curves in class 2601.i do not have complex multiplication.

Modular form 2601.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 4q^{7} - 3q^{8} - 4q^{11} + 2q^{13} - 4q^{14} - q^{16} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.