Properties

Label 4830.l
Number of curves $4$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4830.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.l1 4830l4 \([1, 0, 1, -3014659, 5275646]\) \(3029968325354577848895529/1753440696000000000000\) \(1753440696000000000000\) \([2]\) \(276480\) \(2.7658\)  
4830.l2 4830l2 \([1, 0, 1, -2073844, 1149329042]\) \(986396822567235411402169/6336721794060000\) \(6336721794060000\) \([6]\) \(92160\) \(2.2165\)  
4830.l3 4830l1 \([1, 0, 1, -127124, 18674066]\) \(-227196402372228188089/19338934824115200\) \(-19338934824115200\) \([6]\) \(46080\) \(1.8699\) \(\Gamma_0(N)\)-optimal
4830.l4 4830l3 \([1, 0, 1, 753661, 753662]\) \(47342661265381757089751/27397579603968000000\) \(-27397579603968000000\) \([2]\) \(138240\) \(2.4192\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.