# Properties

 Label 192556i Number of curves $2$ Conductor $192556$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 192556i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
192556.j2 192556i1 $$[0, 0, 0, -116380, 15220917]$$ $$73598976000/336973$$ $$798145561983952$$ $$$$ $$760320$$ $$1.7103$$ $$\Gamma_0(N)$$-optimal
192556.j1 192556i2 $$[0, 0, 0, -177215, -2409066]$$ $$16241202000/9332687$$ $$353682589901758208$$ $$$$ $$1520640$$ $$2.0569$$

## Rank

sage: E.rank()

The elliptic curves in class 192556i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 192556i do not have complex multiplication.

## Modular form 192556.2.a.i

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} - q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 