Properties

Label 574i
Number of curves $2$
Conductor $574$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 574i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
574.g2 574i1 \([1, -1, 1, -19353, 958713]\) \(801581275315909089/70810888830976\) \(70810888830976\) \([7]\) \(3528\) \(1.3978\) \(\Gamma_0(N)\)-optimal
574.g1 574i2 \([1, -1, 1, -9611313, -11466507927]\) \(98191033604529537629349729/10906239337336\) \(10906239337336\) \([]\) \(24696\) \(2.3707\)  

Rank

sage: E.rank()
 

The elliptic curves in class 574i have rank \(1\).

Complex multiplication

The elliptic curves in class 574i do not have complex multiplication.

Modular form 574.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3q^{3} + q^{4} - q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} - q^{10} - 2q^{11} - 3q^{12} + q^{14} + 3q^{15} + q^{16} - 3q^{17} + 6q^{18} - 8q^{19} + O(q^{20})\)  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.