# Properties

 Label 152880.cr Number of curves $2$ Conductor $152880$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cr1")

sage: E.isogeny_class()

## Elliptic curves in class 152880.cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.cr1 152880ct2 $$[0, -1, 0, -36080, -2351040]$$ $$10779215329/1232010$$ $$593693673431040$$ $$[2]$$ $$829440$$ $$1.5671$$
152880.cr2 152880ct1 $$[0, -1, 0, 3120, -187200]$$ $$6967871/35100$$ $$-16914349670400$$ $$[2]$$ $$414720$$ $$1.2205$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 152880.cr have rank $$1$$.

## Complex multiplication

The elliptic curves in class 152880.cr do not have complex multiplication.

## Modular form 152880.2.a.cr

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - 4q^{11} + q^{13} - q^{15} - 8q^{17} - 6q^{19} + O(q^{20})$$

## 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.