Properties

Label 147033.l
Number of curves $4$
Conductor $147033$
CM no
Rank $0$
Graph

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

Elliptic curves in class 147033.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147033.l1 147033l4 \([1, -1, 0, -784356, -267177205]\) \(82483294977/17\) \(10998833118633\) \([2]\) \(967680\) \(1.8897\)  
147033.l2 147033l2 \([1, -1, 0, -49191, -4135168]\) \(20346417/289\) \(186980163016761\) \([2, 2]\) \(483840\) \(1.5431\)  
147033.l3 147033l3 \([1, -1, 0, -5946, -11184103]\) \(-35937/83521\) \(-54037267111843929\) \([2]\) \(967680\) \(1.8897\)  
147033.l4 147033l1 \([1, -1, 0, -5946, 76895]\) \(35937/17\) \(10998833118633\) \([2]\) \(241920\) \(1.1965\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 147033.l have rank \(0\).

Complex multiplication

The elliptic curves in class 147033.l do not have complex multiplication.

Modular form 147033.2.a.l

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