# Properties

 Label 32340.r Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.r1 32340u2 $$[0, -1, 0, -37445, 2801457]$$ $$462893166690304/4125$$ $$51744000$$ $$[]$$ $$46656$$ $$1.0633$$
32340.r2 32340u1 $$[0, -1, 0, -485, 3585]$$ $$1007878144/179685$$ $$2253968640$$ $$[]$$ $$15552$$ $$0.51398$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.r have rank $$1$$.

## Complex multiplication

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

## Modular form 32340.2.a.r

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. 