# Properties

 Label 16830t Number of curves 6 Conductor 16830 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16830.l1")

sage: E.isogeny_class()

## Elliptic curves in class 16830t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.l4 16830t1 [1, -1, 0, -65790, -6478700]  49152 $$\Gamma_0(N)$$-optimal
16830.l3 16830t2 [1, -1, 0, -66510, -6329084] [2, 2] 98304
16830.l2 16830t3 [1, -1, 0, -179010, 20828416] [2, 2] 196608
16830.l5 16830t4 [1, -1, 0, 34470, -23919800]  196608
16830.l1 16830t5 [1, -1, 0, -2629260, 1641423766]  393216
16830.l6 16830t6 [1, -1, 0, 471240, 136963066]  393216

## Rank

sage: E.rank()

The elliptic curves in class 16830t have rank $$1$$.

## Modular form 16830.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} + 6q^{13} + q^{16} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 