Properties

Label 4830m
Number of curves $2$
Conductor $4830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 4830m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.m2 4830m1 \([1, 0, 1, 17, -82]\) \(590589719/3332700\) \(-3332700\) \([2]\) \(1024\) \(-0.066383\) \(\Gamma_0(N)\)-optimal
4830.m1 4830m2 \([1, 0, 1, -213, -1094]\) \(1061520150601/114108750\) \(114108750\) \([2]\) \(2048\) \(0.28019\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} + 4 q^{13} + q^{14} + q^{15} + q^{16} - 4 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.