# Properties

 Label 3648.j Number of curves $2$ Conductor $3648$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 3648.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.j1 3648y1 $$[0, -1, 0, -6113, 185985]$$ $$96386901625/18468$$ $$4841275392$$ $$[2]$$ $$3840$$ $$0.85903$$ $$\Gamma_0(N)$$-optimal
3648.j2 3648y2 $$[0, -1, 0, -5473, 225793]$$ $$-69173457625/42633378$$ $$-11176084242432$$ $$[2]$$ $$7680$$ $$1.2056$$

## Rank

sage: E.rank()

The elliptic curves in class 3648.j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3648.j do not have complex multiplication.

## Modular form3648.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} - 4 q^{7} + q^{9} + 4 q^{11} - 2 q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.