Properties

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

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

Elliptic curves in class 2601.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2601.i1 2601i1 \([1, -1, 0, -207, -752]\) \(274625/81\) \(290107737\) \([2]\) \(768\) \(0.32957\) \(\Gamma_0(N)\)-optimal
2601.i2 2601i2 \([1, -1, 0, 558, -5495]\) \(5359375/6561\) \(-23498726697\) \([2]\) \(1536\) \(0.67614\)  

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