# Properties

 Label 3120.o Number of curves $2$ Conductor $3120$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 3120.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.o1 3120v2 $$[0, 1, 0, -736, 6644]$$ $$10779215329/1232010$$ $$5046312960$$ $$$$ $$2304$$ $$0.59410$$
3120.o2 3120v1 $$[0, 1, 0, 64, 564]$$ $$6967871/35100$$ $$-143769600$$ $$$$ $$1152$$ $$0.24753$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3120.o have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3120.o do not have complex multiplication.

## Modular form3120.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{7} + q^{9} - 4q^{11} - q^{13} - q^{15} + 8q^{17} + 6q^{19} + O(q^{20})$$ ## 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 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. 