# Properties

 Label 19600.dl Number of curves 6 Conductor 19600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.dl1 19600cp6 [0, -1, 0, -53518208, -150677721088] [2] 995328
19600.dl2 19600cp5 [0, -1, 0, -3342208, -2357465088] [2] 497664
19600.dl3 19600cp4 [0, -1, 0, -696208, -183041088] [2] 331776
19600.dl4 19600cp2 [0, -1, 0, -206208, 36086912] [2] 110592
19600.dl5 19600cp1 [0, -1, 0, -10208, 806912] [2] 55296 $$\Gamma_0(N)$$-optimal
19600.dl6 19600cp3 [0, -1, 0, 87792, -16833088] [2] 165888

## Rank

sage: E.rank()

The elliptic curves in class 19600.dl have rank $$1$$.

## Modular form 19600.2.a.dl

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{9} - 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.