# Properties

 Label 37440bs Number of curves $2$ Conductor $37440$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 37440bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.ci2 37440bs1 $$[0, 0, 0, 2292, 117232]$$ $$6967871/35100$$ $$-6707714457600$$ $$$$ $$73728$$ $$1.1434$$ $$\Gamma_0(N)$$-optimal
37440.ci1 37440bs2 $$[0, 0, 0, -26508, 1488112]$$ $$10779215329/1232010$$ $$235440777461760$$ $$$$ $$147456$$ $$1.4900$$

## Rank

sage: E.rank()

The elliptic curves in class 37440bs have rank $$1$$.

## Complex multiplication

The elliptic curves in class 37440bs do not have complex multiplication.

## Modular form 37440.2.a.bs

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} + 4q^{11} + q^{13} - 8q^{17} + 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 