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Properties

Label 2574.p
Number of curves $2$
Conductor $2574$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 2574.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2574.p1 2574o2 \([1, -1, 0, -5553, 160947]\) \(-25979045828113/52635726\) \(-38371444254\) \([3]\) \(5760\) \(0.91779\)  
2574.p2 2574o1 \([1, -1, 0, 117, 1053]\) \(241804367/833976\) \(-607968504\) \([]\) \(1920\) \(0.36849\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2574.p have rank \(0\).

Complex multiplication

The elliptic curves in class 2574.p do not have complex multiplication.

Modular form 2574.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + 5 q^{7} - q^{8} - 3 q^{10} + q^{11} + q^{13} - 5 q^{14} + q^{16} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.