# Properties

 Label 172480.be Number of curves 4 Conductor 172480 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("172480.be1")

sage: E.isogeny_class()

## Elliptic curves in class 172480.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
172480.be1 172480ed4 [0, 1, 0, -1391665, 631438863] [2] 1990656
172480.be2 172480ed3 [0, 1, 0, -87285, 9771355] [2] 995328
172480.be3 172480ed2 [0, 1, 0, -19665, 593263] [2] 663552
172480.be4 172480ed1 [0, 1, 0, -8885, -318725] [2] 331776 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 172480.be have rank $$2$$.

## Modular form 172480.2.a.be

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + q^{9} + q^{11} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.