Properties

Label 154.c
Number of curves $4$
Conductor $154$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154.c1 154b3 \([1, -1, 1, -5164, -141529]\) \(15226621995131793/2324168\) \(2324168\) \([2]\) \(96\) \(0.62717\)  
154.c2 154b4 \([1, -1, 1, -604, 2343]\) \(24331017010833/12004097336\) \(12004097336\) \([2]\) \(96\) \(0.62717\)  
154.c3 154b2 \([1, -1, 1, -324, -2137]\) \(3750606459153/45914176\) \(45914176\) \([2, 2]\) \(48\) \(0.28060\)  
154.c4 154b1 \([1, -1, 1, -4, -89]\) \(-5545233/3469312\) \(-3469312\) \([4]\) \(24\) \(-0.065974\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154.c have rank \(0\).

Complex multiplication

The elliptic curves in class 154.c do not have complex multiplication.

Modular form 154.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} - q^{7} + q^{8} - 3 q^{9} + 2 q^{10} - q^{11} + 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - 3 q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.