# Properties

 Label 32490ba Number of curves 8 Conductor 32490 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32490.n1")

sage: E.isogeny_class()

## Elliptic curves in class 32490ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.n8 32490ba1 [1, -1, 0, 4806, 392548] [2] 110592 $$\Gamma_0(N)$$-optimal
32490.n6 32490ba2 [1, -1, 0, -60174, 5162080] [2, 2] 221184
32490.n7 32490ba3 [1, -1, 0, -43929, -11586515] [2] 331776
32490.n5 32490ba4 [1, -1, 0, -222624, -34768130] [2] 442368
32490.n4 32490ba5 [1, -1, 0, -937404, 349562578] [2] 442368
32490.n3 32490ba6 [1, -1, 0, -1083609, -433072787] [2, 2] 663552
32490.n1 32490ba7 [1, -1, 0, -17328609, -27760411787] [2] 1327104
32490.n2 32490ba8 [1, -1, 0, -1473489, -93331355] [2] 1327104

## Rank

sage: E.rank()

The elliptic curves in class 32490ba have rank $$2$$.

## Modular form 32490.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - 4q^{7} - q^{8} - q^{10} - 2q^{13} + 4q^{14} + q^{16} - 6q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.