# Properties

 Label 600.h Number of curves 6 Conductor 600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("600.h1")

sage: E.isogeny_class()

## Elliptic curves in class 600.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
600.h1 600d5 [0, 1, 0, -9608, -365712] [2] 512
600.h2 600d4 [0, 1, 0, -1608, 24288] [2] 256
600.h3 600d3 [0, 1, 0, -608, -5712] [2, 2] 256
600.h4 600d2 [0, 1, 0, -108, 288] [2, 2] 128
600.h5 600d1 [0, 1, 0, 17, 38] [2] 64 $$\Gamma_0(N)$$-optimal
600.h6 600d6 [0, 1, 0, 392, -21712] [2] 512

## Rank

sage: E.rank()

The elliptic curves in class 600.h have rank $$0$$.

## Modular form600.2.a.h

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.