# Properties

 Label 40425.cl Number of curves 6 Conductor 40425 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40425.cl1")

sage: E.isogeny_class()

## Elliptic curves in class 40425.cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40425.cl1 40425k6 [1, 1, 0, -5535800, 5010934125] [2] 983040
40425.cl2 40425k4 [1, 1, 0, -347925, 77265000] [2, 2] 491520
40425.cl3 40425k2 [1, 1, 0, -47800, -2268125] [2, 2] 245760
40425.cl4 40425k1 [1, 1, 0, -41675, -3291000] [2] 122880 $$\Gamma_0(N)$$-optimal
40425.cl5 40425k5 [1, 1, 0, 37950, 239718375] [2] 983040
40425.cl6 40425k3 [1, 1, 0, 154325, -16214750] [2] 491520

## Rank

sage: E.rank()

The elliptic curves in class 40425.cl have rank $$0$$.

## Modular form 40425.2.a.cl

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{6} - 3q^{8} + q^{9} - q^{11} + q^{12} + 6q^{13} - q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.