# Properties

 Label 188760bn Number of curves $4$ Conductor $188760$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 188760bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.ba4 188760bn1 $$[0, -1, 0, -11054116, -19252754684]$$ $$-329381898333928144/162600887109375$$ $$-73742691883103100000000$$ $$[2]$$ $$20643840$$ $$3.0931$$ $$\Gamma_0(N)$$-optimal
188760.ba3 188760bn2 $$[0, -1, 0, -194066616, -1040389299684]$$ $$445574312599094932036/61129333175625$$ $$110893406832582042240000$$ $$[2, 2]$$ $$41287680$$ $$3.4397$$
188760.ba2 188760bn3 $$[0, -1, 0, -211369616, -843820298484]$$ $$287849398425814280018/81784533026485575$$ $$296727120103288446428313600$$ $$[2]$$ $$82575360$$ $$3.7863$$
188760.ba1 188760bn4 $$[0, -1, 0, -3104963616, -66592625380884]$$ $$912446049969377120252018/17177299425$$ $$62321937913144166400$$ $$[2]$$ $$82575360$$ $$3.7863$$

## Rank

sage: E.rank()

The elliptic curves in class 188760bn have rank $$1$$.

## Complex multiplication

The elliptic curves in class 188760bn do not have complex multiplication.

## Modular form 188760.2.a.bn

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 4 q^{7} + q^{9} - q^{13} + q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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 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.