# Properties

 Label 161700.el Number of curves 2 Conductor 161700 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("161700.el1")

sage: E.isogeny_class()

## Elliptic curves in class 161700.el

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
161700.el1 161700bc2 [0, 1, 0, -15108, 334788] [2] 552960
161700.el2 161700bc1 [0, 1, 0, 3267, 40788] [2] 276480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 161700.el have rank $$1$$.

## Modular form 161700.2.a.el

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.