Properties

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

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.bh1 4830bg2 \([1, 0, 0, -230, 1302]\) \(1345938541921/24850350\) \(24850350\) \([2]\) \(1536\) \(0.21355\)  
4830.bh2 4830bg1 \([1, 0, 0, 0, 60]\) \(-1/1555260\) \(-1555260\) \([2]\) \(768\) \(-0.13302\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.bh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.