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Properties

Label 4998i
Number of curves $2$
Conductor $4998$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4998i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.b2 4998i1 \([1, 1, 0, -8796, -8236080]\) \(-1865409391/724451328\) \(-29234224180740096\) \([2]\) \(56448\) \(1.8387\) \(\Gamma_0(N)\)-optimal
4998.b1 4998i2 \([1, 1, 0, -667356, -208043184]\) \(814544990575471/9268826496\) \(374030581770771072\) \([2]\) \(112896\) \(2.1852\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4998i have rank \(1\).

Complex multiplication

The elliptic curves in class 4998i do not have complex multiplication.

Modular form 4998.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} - q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.