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Properties

Label 28830.j
Number of curves $2$
Conductor $28830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 28830.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28830.j1 28830i2 \([1, 1, 0, -502142, 136775964]\) \(-15777367606441/3574920\) \(-3172754659280520\) \([]\) \(345600\) \(1.9666\)  
28830.j2 28830i1 \([1, 1, 0, 2383, 655119]\) \(1685159/209250\) \(-185710145249250\) \([]\) \(115200\) \(1.4173\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28830.j have rank \(1\).

Complex multiplication

The elliptic curves in class 28830.j do not have complex multiplication.

Modular form 28830.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 3 q^{11} - q^{12} - 2 q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + 5 q^{19} + O(q^{20})\) 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.