# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bl1 32340bj2 $$[0, 1, 0, -1738340, 714049188]$$ $$19288565375865424/3837216796875$$ $$115569848047500000000$$ $$$$ $$829440$$ $$2.5660$$
32340.bl2 32340bj1 $$[0, 1, 0, 226315, 66498900]$$ $$681010157060096/1406657896875$$ $$-2647870318551150000$$ $$$$ $$414720$$ $$2.2194$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - q^{11} - 2q^{13} + q^{15} - 2q^{17} + O(q^{20})$$ ## 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. 