# Properties

 Label 3920.g Number of curves $2$ Conductor $3920$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.g1 3920bg2 $$[0, 1, 0, -384960, -92065100]$$ $$-5452947409/250$$ $$-289254654976000$$ $$[]$$ $$30240$$ $$1.8505$$
3920.g2 3920bg1 $$[0, 1, 0, -800, -327692]$$ $$-49/40$$ $$-46280744796160$$ $$[]$$ $$10080$$ $$1.3012$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3920.g do not have complex multiplication.

## Modular form3920.2.a.g

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 