# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bn1")

sage: E.isogeny_class()

## Elliptic curves in class 327990.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bn1 327990bn4 $$[1, 0, 0, -7024470, -6561320400]$$ $$64443098670429961/6032611833300$$ $$3588338204987404389300$$ $$$$ $$41287680$$ $$2.8744$$
327990.bn2 327990bn2 $$[1, 0, 0, -1557970, 633686900]$$ $$703093388853961/115124490000$$ $$68478731470231290000$$ $$[2, 2]$$ $$20643840$$ $$2.5278$$
327990.bn3 327990bn1 $$[1, 0, 0, -1490690, 700388292]$$ $$615882348586441/21715200$$ $$12916707380179200$$ $$$$ $$10321920$$ $$2.1812$$ $$\Gamma_0(N)$$-optimal
327990.bn4 327990bn3 $$[1, 0, 0, 2832050, 3560074232]$$ $$4223169036960119/11647532812500$$ $$-6928224148987720312500$$ $$$$ $$41287680$$ $$2.8744$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 327990.2.a.bn

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} + q^{13} - 4q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 