# Properties

 Label 116688.n Number of curves $2$ Conductor $116688$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 116688.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116688.n1 116688l1 $$[0, -1, 0, -1496, 16368]$$ $$90458382169/25788048$$ $$105627844608$$ $$$$ $$153600$$ $$0.82190$$ $$\Gamma_0(N)$$-optimal
116688.n2 116688l2 $$[0, -1, 0, 3944, 103408]$$ $$1656015369191/2114999172$$ $$-8663036608512$$ $$$$ $$307200$$ $$1.1685$$

## Rank

sage: E.rank()

The elliptic curves in class 116688.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 116688.n do not have complex multiplication.

## Modular form 116688.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{5} + q^{9} - q^{11} - q^{13} - 4q^{15} + q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 