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Properties

Label 4830.be
Number of curves $8$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.be1 4830bc7 \([1, 0, 0, -253899016, -1461052982200]\) \(1810117493172631097464564372609/125368453502655029296875000\) \(125368453502655029296875000\) \([2]\) \(1990656\) \(3.7557\)  
4830.be2 4830bc6 \([1, 0, 0, -249518896, -1517075593024]\) \(1718043013877225552292911401729/9180538178765625000000\) \(9180538178765625000000\) \([2, 2]\) \(995328\) \(3.4092\)  
4830.be3 4830bc3 \([1, 0, 0, -249518576, -1517079678720]\) \(1718036403880129446396978632449/49057344000000\) \(49057344000000\) \([2]\) \(497664\) \(3.0626\)  
4830.be4 4830bc8 \([1, 0, 0, -245143896, -1572836718024]\) \(-1629247127728109256861881401729/125809119536174660320875000\) \(-125809119536174660320875000\) \([2]\) \(1990656\) \(3.7557\)  
4830.be5 4830bc4 \([1, 0, 0, -47316976, 124844147456]\) \(11715873038622856702991202049/46415372499833400000000\) \(46415372499833400000000\) \([6]\) \(663552\) \(3.2064\)  
4830.be6 4830bc2 \([1, 0, 0, -4393456, -140558080]\) \(9378698233516887309850369/5418996968417034240000\) \(5418996968417034240000\) \([2, 6]\) \(331776\) \(2.8599\)  
4830.be7 4830bc1 \([1, 0, 0, -3082736, -2078064384]\) \(3239908336204082689644289/9880281924658790400\) \(9880281924658790400\) \([6]\) \(165888\) \(2.5133\) \(\Gamma_0(N)\)-optimal
4830.be8 4830bc5 \([1, 0, 0, 17558544, -1119617280]\) \(598672364899527954087397631/346996861747253448998400\) \(-346996861747253448998400\) \([6]\) \(663552\) \(3.2064\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.be

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.