Properties

Label 154560.n
Number of curves $4$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 154560.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.n1 154560dp4 \([0, -1, 0, -2362886401, -44206810293599]\) \(5565604209893236690185614401/229307220930246900000\) \(60111512123538643353600000\) \([2]\) \(117964800\) \(4.0279\)  
154560.n2 154560dp3 \([0, -1, 0, -720369921, 6863025539745]\) \(157706830105239346386477121/13650704956054687500000\) \(3578450400000000000000000000\) \([2]\) \(117964800\) \(4.0279\)  
154560.n3 154560dp2 \([0, -1, 0, -154886401, -619565493599]\) \(1567558142704512417614401/274462175610000000000\) \(71948612563107840000000000\) \([2, 2]\) \(58982400\) \(3.6813\)  
154560.n4 154560dp1 \([0, -1, 0, 18456319, -55473614175]\) \(2652277923951208297919/6605028468326400000\) \(-1731468582800955801600000\) \([2]\) \(29491200\) \(3.3348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154560.n have rank \(0\).

Complex multiplication

The elliptic curves in class 154560.n do not have complex multiplication.

Modular form 154560.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 6 q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.