# Properties

 Label 262080.b Number of curves 4 Conductor 262080 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.b1")

sage: E.isogeny_class()

## Elliptic curves in class 262080.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.b1 262080b4 [0, 0, 0, -80991468, 280547898192]  15925248
262080.b2 262080b3 [0, 0, 0, -5063148, 4381412688]  7962624
262080.b3 262080b2 [0, 0, 0, -1023468, 365741392]  5308416
262080.b4 262080b1 [0, 0, 0, -224748, -34577072]  2654208 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 262080.b have rank $$0$$.

## Modular form 262080.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} - q^{13} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 