# Properties

 Label 116886t Number of curves $2$ Conductor $116886$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 116886t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.v2 116886t1 $$[1, 0, 1, -19121, -1475476]$$ $$-52802213121625/33540304392$$ $$-491063596603272$$ $$$$ $$601344$$ $$1.5204$$ $$\Gamma_0(N)$$-optimal
116886.v1 116886t2 $$[1, 0, 1, -1734296, -879233434]$$ $$-39402364010111991625/3532128768$$ $$-51713897292288$$ $$[]$$ $$1804032$$ $$2.0697$$

## Rank

sage: E.rank()

The elliptic curves in class 116886t have rank $$0$$.

## Complex multiplication

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

## Modular form 116886.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{12} - q^{13} - q^{14} + q^{16} - 6q^{17} - q^{18} + 5q^{19} + O(q^{20})$$ ## 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. 