# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("em1")

sage: E.isogeny_class()

## Elliptic curves in class 37440em

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.m2 37440em1 $$[0, 0, 0, 2292, -117232]$$ $$6967871/35100$$ $$-6707714457600$$ $$$$ $$73728$$ $$1.1434$$ $$\Gamma_0(N)$$-optimal
37440.m1 37440em2 $$[0, 0, 0, -26508, -1488112]$$ $$10779215329/1232010$$ $$235440777461760$$ $$$$ $$147456$$ $$1.4900$$

## Rank

sage: E.rank()

The elliptic curves in class 37440em have rank $$2$$.

## Complex multiplication

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

## Modular form 37440.2.a.em

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. 