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Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2574d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2574.j1 2574d1 \([1, -1, 0, -51969609, -144342625779]\) \(-21293376668673906679951249/26211168887701209984\) \(-19107942119134182078336\) \([]\) \(282240\) \(3.1851\) \(\Gamma_0(N)\)-optimal
2574.j2 2574d2 \([1, -1, 0, 147177801, 9059661330291]\) \(483641001192506212470106511/48918776756543177755473774\) \(-35661788255519976583740381246\) \([]\) \(1975680\) \(4.1581\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2574.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - q^{11} - q^{13} - q^{14} + q^{16} - 4 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.