# Properties

 Label 327990.bl Number of curves $4$ Conductor $327990$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 327990.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bl1 327990bl4 $$[1, 0, 0, -406641, -99824049]$$ $$12501706118329/2570490$$ $$1528987398397290$$ $$$$ $$2867200$$ $$1.9107$$
327990.bl2 327990bl2 $$[1, 0, 0, -28191, -1199979]$$ $$4165509529/1368900$$ $$814253644116900$$ $$[2, 2]$$ $$1433600$$ $$1.5641$$
327990.bl3 327990bl1 $$[1, 0, 0, -11371, 451745]$$ $$273359449/9360$$ $$5567546284560$$ $$$$ $$716800$$ $$1.2175$$ $$\Gamma_0(N)$$-optimal
327990.bl4 327990bl3 $$[1, 0, 0, 81139, -8218965]$$ $$99317171591/106616250$$ $$-63417831897566250$$ $$$$ $$2867200$$ $$1.9107$$

## Rank

sage: E.rank()

The elliptic curves in class 327990.bl have rank $$1$$.

## Complex multiplication

The elliptic curves in class 327990.bl do not have complex multiplication.

## Modular form 327990.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + q^{12} - q^{13} - q^{15} + q^{16} + 6q^{17} + q^{18} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 