# Properties

 Label 3920.e Number of curves $2$ Conductor $3920$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.e1 3920x2 $$[0, 1, 0, -2536, -86220]$$ $$-8990558521/10485760$$ $$-2104533975040$$ $$[]$$ $$6048$$ $$1.0587$$
3920.e2 3920x1 $$[0, 1, 0, 264, 2260]$$ $$10100279/16000$$ $$-3211264000$$ $$[]$$ $$2016$$ $$0.50937$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.e have rank $$1$$.

## Complex multiplication

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

## Modular form3920.2.a.e

sage: E.q_eigenform(10)

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