# Properties

 Label 37570.o Number of curves $2$ Conductor $37570$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 37570.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.o1 37570g2 $$[1, 1, 1, -51132181, 140706167803]$$ $$3009261308803109129809313/85820312500000000$$ $$421635195312500000000$$ $$$$ $$2949120$$ $$3.0589$$
37570.o2 37570g1 $$[1, 1, 1, -3325461, 2009311739]$$ $$827813553991775477153/123566310400000000$$ $$607081282995200000000$$ $$$$ $$1474560$$ $$2.7123$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 37570.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 37570.o do not have complex multiplication.

## Modular form 37570.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} + q^{8} + q^{9} - q^{10} + 2q^{12} - q^{13} - 2q^{15} + q^{16} + q^{18} + O(q^{20})$$ ## 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. 