# Properties

 Label 40950.dh Number of curves 8 Conductor 40950 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40950.dh1")

sage: E.isogeny_class()

## Elliptic curves in class 40950.dh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40950.dh1 40950dm8 [1, -1, 1, -9042852380, 330985708384497] [2] 21233664
40950.dh2 40950dm6 [1, -1, 1, -565178630, 5171750824497] [2, 2] 10616832
40950.dh3 40950dm7 [1, -1, 1, -558232880, 5305053658497] [2] 21233664
40950.dh4 40950dm5 [1, -1, 1, -111691130, 453616474497] [2] 7077888
40950.dh5 40950dm3 [1, -1, 1, -35758130, 78725614497] [2] 5308416
40950.dh6 40950dm2 [1, -1, 1, -9316130, 1937974497] [2, 2] 3538944
40950.dh7 40950dm1 [1, -1, 1, -5788130, -5329705503] [2] 1769472 $$\Gamma_0(N)$$-optimal
40950.dh8 40950dm4 [1, -1, 1, 36610870, 15348658497] [2] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 40950.dh have rank $$1$$.

## Modular form 40950.2.a.dh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - q^{13} - q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.