# Properties

 Label 1638.t Number of curves $2$ Conductor $1638$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("t1")

E.isogeny_class()

## Elliptic curves in class 1638.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.t1 1638n2 $$[1, -1, 1, -191, -1511]$$ $$-38958219/30758$$ $$-605409714$$ $$[]$$ $$864$$ $$0.38364$$
1638.t2 1638n1 $$[1, -1, 1, 19, 29]$$ $$29503629/35672$$ $$-963144$$ $$[3]$$ $$288$$ $$-0.16566$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1638.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1638.t do not have complex multiplication.

## Modular form1638.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} + 3 q^{11} + q^{13} + q^{14} + q^{16} - 3 q^{17} + 5 q^{19} + O(q^{20})$$

## 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.