# Properties

 Label 4140.j Number of curves $2$ Conductor $4140$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 4140.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4140.j1 4140g1 $$[0, 0, 0, -192, 1001]$$ $$67108864/1725$$ $$20120400$$ $$[2]$$ $$960$$ $$0.18363$$ $$\Gamma_0(N)$$-optimal
4140.j2 4140g2 $$[0, 0, 0, 33, 3206]$$ $$21296/23805$$ $$-4442584320$$ $$[2]$$ $$1920$$ $$0.53021$$

## Rank

sage: E.rank()

The elliptic curves in class 4140.j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4140.j do not have complex multiplication.

## Modular form4140.2.a.j

sage: E.q_eigenform(10)

$$q + q^{5} - 6 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.