Properties

Label 4830x
Number of curves $2$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 4830x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.w1 4830x1 \([1, 1, 1, -5165, -144925]\) \(15238420194810961/12619514880\) \(12619514880\) \([2]\) \(6720\) \(0.86658\) \(\Gamma_0(N)\)-optimal
4830.w2 4830x2 \([1, 1, 1, -4045, -208093]\) \(-7319577278195281/14169067365600\) \(-14169067365600\) \([2]\) \(13440\) \(1.2132\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4830x have rank \(0\).

Complex multiplication

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

Modular form 4830.2.a.x

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