# Properties

 Label 29040.b Number of curves 8 Conductor 29040 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("29040.b1")

sage: E.isogeny_class()

## Elliptic curves in class 29040.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29040.b1 29040ch7 [0, -1, 0, -10325696, -12767623680] [2] 829440
29040.b2 29040ch8 [0, -1, 0, -878016, -42806784] [2] 829440
29040.b3 29040ch6 [0, -1, 0, -645696, -199111680] [2, 2] 414720
29040.b4 29040ch5 [0, -1, 0, -558576, 160868160] [2] 276480
29040.b5 29040ch4 [0, -1, 0, -132656, -15973824] [2] 276480
29040.b6 29040ch2 [0, -1, 0, -35856, 2379456] [2, 2] 138240
29040.b7 29040ch3 [0, -1, 0, -26176, -5325824] [2] 207360
29040.b8 29040ch1 [0, -1, 0, 2864, 180160] [2] 69120 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 29040.b have rank $$1$$.

## Modular form 29040.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 4q^{7} + q^{9} - 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.