# Properties

 Label 1850.o Number of curves $3$ Conductor $1850$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 1850.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.o1 1850h1 $$[1, 1, 1, -1338, 18281]$$ $$-16954786009/370$$ $$-5781250$$ $$[]$$ $$864$$ $$0.41351$$ $$\Gamma_0(N)$$-optimal
1850.o2 1850h2 $$[1, 1, 1, -463, 42781]$$ $$-702595369/50653000$$ $$-791453125000$$ $$[]$$ $$2592$$ $$0.96281$$
1850.o3 1850h3 $$[1, 1, 1, 4162, -1150469]$$ $$510273943271/37000000000$$ $$-578125000000000$$ $$[]$$ $$7776$$ $$1.5121$$

## Rank

sage: E.rank()

The elliptic curves in class 1850.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1850.o do not have complex multiplication.

## Modular form1850.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} + q^{16} - 3 q^{17} + q^{18} + 2 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 