Number of curves $2$
Conductor $439569$
CM no
Rank $0$

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

Elliptic curves in class

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.ba1 439569ba2 [1, -1, 1, -518261009, -4541072067372] [2] 70189056  
439569.ba2 439569ba1 [1, -1, 1, -32537264, -70276428894] [2] 35094528 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 439569.ba1.


sage: E.rank()

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

Complex multiplication

The elliptic curves in class do not have complex multiplication.

Modular form

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