# Properties

 Label 16900j Number of curves 4 Conductor 16900 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16900.p1")

sage: E.isogeny_class()

## Elliptic curves in class 16900j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16900.p3 16900j1 [0, -1, 0, -5633, 113762]  27648 $$\Gamma_0(N)$$-optimal
16900.p4 16900j2 [0, -1, 0, 15492, 747512]  55296
16900.p1 16900j3 [0, -1, 0, -174633, -28024738]  82944
16900.p2 16900j4 [0, -1, 0, -153508, -35080488]  165888

## Rank

sage: E.rank()

The elliptic curves in class 16900j have rank $$0$$.

## Modular form 16900.2.a.p

sage: E.q_eigenform(10)

$$q + 2q^{3} + 2q^{7} + q^{9} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 