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Properties

Label 28611.i
Number of curves $2$
Conductor $28611$
CM no
Rank $0$
Graph

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

Elliptic curves in class 28611.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28611.i1 28611e2 \([1, -1, 1, -4823, 129404]\) \(19034163/121\) \(78857437923\) \([2]\) \(40960\) \(0.92792\)  
28611.i2 28611e1 \([1, -1, 1, -488, -646]\) \(19683/11\) \(7168857993\) \([2]\) \(20480\) \(0.58134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28611.i have rank \(0\).

Complex multiplication

The elliptic curves in class 28611.i do not have complex multiplication.

Modular form 28611.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - 6 q^{19} + O(q^{20})\) 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.