# Properties

 Label 32340.bh Number of curves $2$ Conductor $32340$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bh1 32340y2 $$[0, 1, 0, -1834821, -957230121]$$ $$462893166690304/4125$$ $$6087629856000$$ $$[]$$ $$326592$$ $$2.0362$$
32340.bh2 32340y1 $$[0, 1, 0, -23781, -1182105]$$ $$1007878144/179685$$ $$265177156527360$$ $$[3]$$ $$108864$$ $$1.4869$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.bh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 32340.bh do not have complex multiplication.

## Modular form 32340.2.a.bh

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.