# Properties

 Label 327990.o Number of curves $2$ Conductor $327990$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 327990.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.o1 327990o1 $$[1, 0, 1, -63934, 7009232]$$ $$-40861808665609/6406452000$$ $$-4531161777012000$$ $$$$ $$2268000$$ $$1.7327$$ $$\Gamma_0(N)$$-optimal
327990.o2 327990o2 $$[1, 0, 1, 428051, -25264984]$$ $$12263649421047431/7488000000000$$ $$-5296120128000000000$$ $$[]$$ $$6804000$$ $$2.2820$$

## Rank

sage: E.rank()

The elliptic curves in class 327990.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 327990.o do not have complex multiplication.

## Modular form 327990.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} - 2q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 