Properties

Label 439569i
Number of curves $2$
Conductor $439569$
CM no
Rank $0$
Graph

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

Elliptic curves in class 439569i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.i2 439569i1 [1, -1, 1, -322066712, -2220967201670] [2] 185794560 \(\Gamma_0(N)\)-optimal
439569.i1 439569i2 [1, -1, 1, -5150732177, -142281237679460] [2] 371589120  

Rank

sage: E.rank()
 

The elliptic curves in class 439569i have rank \(0\).

Complex multiplication

The elliptic curves in class 439569i do not have complex multiplication.

Modular form 439569.2.a.i

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.