Properties

Label 47753.i
Number of curves $4$
Conductor $47753$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 47753.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47753.i1 47753f4 \([1, -1, 0, -254741, -49423960]\) \(82483294977/17\) \(376794139193\) \([2]\) \(149760\) \(1.6085\)  
47753.i2 47753f2 \([1, -1, 0, -15976, -763653]\) \(20346417/289\) \(6405500366281\) \([2, 2]\) \(74880\) \(1.2619\)  
47753.i3 47753f3 \([1, -1, 0, -1931, -2069838]\) \(-35937/83521\) \(-1851189605855209\) \([2]\) \(149760\) \(1.6085\)  
47753.i4 47753f1 \([1, -1, 0, -1931, 14440]\) \(35937/17\) \(376794139193\) \([2]\) \(37440\) \(0.91536\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47753.i have rank \(0\).

Complex multiplication

The elliptic curves in class 47753.i do not have complex multiplication.

Modular form 47753.2.a.i

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.