# Properties

 Label 76050bc Number of curves $6$ Conductor $76050$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76050.bs1")

sage: E.isogeny_class()

## Elliptic curves in class 76050bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76050.bs6 76050bc1 [1, -1, 0, 569583, -66404259] [2] 2064384 $$\Gamma_0(N)$$-optimal
76050.bs5 76050bc2 [1, -1, 0, -2472417, -550082259] [2, 2] 4128768
76050.bs3 76050bc3 [1, -1, 0, -21484917, 37950230241] [2, 2] 8257536
76050.bs2 76050bc4 [1, -1, 0, -32131917, -70042290759] [2] 8257536
76050.bs4 76050bc5 [1, -1, 0, -4373667, 96727373991] [2] 16515072
76050.bs1 76050bc6 [1, -1, 0, -342796167, 2442964936491] [2] 16515072

## Rank

sage: E.rank()

The elliptic curves in class 76050bc have rank $$0$$.

## Modular form 76050.2.a.bs

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} + 4q^{11} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.