# Properties

 Label 32340.l Number of curves $2$ Conductor $32340$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.l1 32340k2 $$[0, -1, 0, -71010620, 230315561400]$$ $$1314817350433665559504/190690249278375$$ $$5743236387161994336000$$ $$$$ $$3870720$$ $$3.1901$$
32340.l2 32340k1 $$[0, -1, 0, -4033745, 4282003650]$$ $$-3856034557002072064/1973796785296875$$ $$-3715443487894272750000$$ $$$$ $$1935360$$ $$2.8436$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - q^{11} - q^{15} + 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 