Properties

Label 4598.a
Number of curves $2$
Conductor $4598$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4598.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.a1 4598k2 \([1, 1, 0, -8472, 328750]\) \(-37966934881/4952198\) \(-8773120841078\) \([]\) \(14000\) \(1.2167\)  
4598.a2 4598k1 \([1, 1, 0, -2, -1580]\) \(-1/608\) \(-1077109088\) \([]\) \(2800\) \(0.41201\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4598.a have rank \(1\).

Complex multiplication

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

Modular form 4598.2.a.a

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.