Properties

Label 4598.i
Number of curves $2$
Conductor $4598$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4598.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.i1 4598a2 \([1, 1, 0, -28921, -1903095]\) \(1134626507/1444\) \(3404876465804\) \([2]\) \(23232\) \(1.3128\)  
4598.i2 4598a1 \([1, 1, 0, -2301, -13075]\) \(571787/304\) \(716816098064\) \([2]\) \(11616\) \(0.96624\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4598.i have rank \(0\).

Complex multiplication

The elliptic curves in class 4598.i do not have complex multiplication.

Modular form 4598.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{10} + 2 q^{12} - 6 q^{13} + 4 q^{14} - 4 q^{15} + q^{16} - 4 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.