# Properties

 Label 190575er Number of curves $2$ Conductor $190575$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("er1")

sage: E.isogeny_class()

## Elliptic curves in class 190575er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.ev2 190575er1 [0, 0, 1, -243400575, 1711662797281] [] 138240000 $$\Gamma_0(N)$$-optimal
190575.ev1 190575er2 [0, 0, 1, -729366825, -143336942153969] [] 691200000

## Rank

sage: E.rank()

The elliptic curves in class 190575er have rank $$0$$.

## Complex multiplication

The elliptic curves in class 190575er do not have complex multiplication.

## Modular form 190575.2.a.er

sage: E.q_eigenform(10)

$$q + 2q^{2} + 2q^{4} + q^{7} - 6q^{13} + 2q^{14} - 4q^{16} + 7q^{17} + 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.