# Properties

 Label 369600.gh Number of curves 6 Conductor 369600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("369600.gh1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.gh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.gh1 369600gh6 [0, -1, 0, -7230433, -7480911263] [2] 10485760
369600.gh2 369600gh4 [0, -1, 0, -454433, -115399263] [2, 2] 5242880
369600.gh3 369600gh2 [0, -1, 0, -62433, 3376737] [2, 2] 2621440
369600.gh4 369600gh1 [0, -1, 0, -54433, 4904737] [2] 1310720 $$\Gamma_0(N)$$-optimal
369600.gh5 369600gh5 [0, -1, 0, 49567, -357823263] [2] 10485760
369600.gh6 369600gh3 [0, -1, 0, 201567, 24232737] [2] 5242880

## Rank

sage: E.rank()

The elliptic curves in class 369600.gh have rank $$0$$.

## Modular form 369600.2.a.gh

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} + q^{11} + 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.