Properties

Label 4830.o
Number of curves $4$
Conductor $4830$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4830.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.o1 4830q3 \([1, 0, 1, -491963, -75523594]\) \(13167998447866683762601/5158996582031250000\) \(5158996582031250000\) \([2]\) \(122880\) \(2.2892\)  
4830.o2 4830q2 \([1, 0, 1, -221483, 39268118]\) \(1201550658189465626281/28577902500000000\) \(28577902500000000\) \([2, 2]\) \(61440\) \(1.9427\)  
4830.o3 4830q1 \([1, 0, 1, -220203, 39754006]\) \(1180838681727016392361/692428800000\) \(692428800000\) \([2]\) \(30720\) \(1.5961\) \(\Gamma_0(N)\)-optimal
4830.o4 4830q4 \([1, 0, 1, 28517, 122968118]\) \(2564821295690373719/6533572090396050000\) \(-6533572090396050000\) \([4]\) \(122880\) \(2.2892\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4830.o have rank \(1\).

Complex multiplication

The elliptic curves in class 4830.o do not have complex multiplication.

Modular form 4830.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} - 2q^{13} - q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.