# Properties

 Label 32490bv Number of curves $4$ Conductor $32490$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bv1")

sage: E.isogeny_class()

## Elliptic curves in class 32490bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bu3 32490bv1 $$[1, -1, 1, -100787, 12267011]$$ $$3301293169/22800$$ $$781958997277200$$ $$[4]$$ $$184320$$ $$1.6913$$ $$\Gamma_0(N)$$-optimal
32490.bu2 32490bv2 $$[1, -1, 1, -165767, -5433541]$$ $$14688124849/8122500$$ $$278572892780002500$$ $$[2, 2]$$ $$368640$$ $$2.0379$$
32490.bu4 32490bv3 $$[1, -1, 1, 646483, -43446841]$$ $$871257511151/527800050$$ $$-18101666572844562450$$ $$[2]$$ $$737280$$ $$2.3844$$
32490.bu1 32490bv4 $$[1, -1, 1, -2017697, -1101035329]$$ $$26487576322129/44531250$$ $$1527263666557031250$$ $$[2]$$ $$737280$$ $$2.3844$$

## Rank

sage: E.rank()

The elliptic curves in class 32490bv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32490bv do not have complex multiplication.

## Modular form 32490.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} - 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.