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Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439569ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.ba2 439569ba1 [1, -1, 1, -32537264, -70276428894] [2] 35094528 \(\Gamma_0(N)\)-optimal
439569.ba1 439569ba2 [1, -1, 1, -518261009, -4541072067372] [2] 70189056  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 439569.2.a.ba

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

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.