# Properties

 Label 116886m Number of curves $2$ Conductor $116886$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 116886m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.k2 116886m1 $$[1, 0, 1, 360, -11618]$$ $$2924207/34776$$ $$-61607805336$$ $$[]$$ $$172800$$ $$0.75124$$ $$\Gamma_0(N)$$-optimal
116886.k1 116886m2 $$[1, 0, 1, -3270, 328150]$$ $$-2181825073/25039686$$ $$-44359331169846$$ $$[]$$ $$518400$$ $$1.3005$$

## Rank

sage: E.rank()

The elliptic curves in class 116886m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 116886m do not have complex multiplication.

## Modular form 116886.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 3q^{10} + q^{12} - 5q^{13} + q^{14} - 3q^{15} + q^{16} - q^{18} - 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 