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Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 4598.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.q1 4598m1 \([1, 0, 0, -8, -10]\) \(-471625/38\) \(-4598\) \([]\) \(288\) \(-0.55080\) \(\Gamma_0(N)\)-optimal
4598.q2 4598m2 \([1, 0, 0, 47, 1]\) \(94766375/54872\) \(-6639512\) \([]\) \(864\) \(-0.0014900\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4598.2.a.q

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.