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Properties

Label 48841b
Number of curves $2$
Conductor $48841$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 48841b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48841.d2 48841b1 \([1, -1, 0, -35785190, 82269972903]\) \(43499078731809/82055753\) \(9560105332599896007713\) \([2]\) \(5806080\) \(3.1077\) \(\Gamma_0(N)\)-optimal
48841.d1 48841b2 \([1, -1, 0, -572303575, 5269866237468]\) \(177930109857804849/634933\) \(73974415409284584493\) \([2]\) \(11612160\) \(3.4543\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48841b have rank \(1\).

Complex multiplication

The elliptic curves in class 48841b do not have complex multiplication.

Modular form 48841.2.a.b

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