# Properties

 Label 3120.v Number of curves $2$ Conductor $3120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 3120.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.v1 3120i2 $$[0, 1, 0, -4280, 74100]$$ $$4234737878642/1247410125$$ $$2554695936000$$ $$$$ $$3840$$ $$1.0865$$
3120.v2 3120i1 $$[0, 1, 0, 720, 8100]$$ $$40254822716/49359375$$ $$-50544000000$$ $$$$ $$1920$$ $$0.73996$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3120.2.a.v

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 