# Properties

 Label 3600bk Number of curves 8 Conductor 3600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3600.f1")

sage: E.isogeny_class()

## Elliptic curves in class 3600bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.f8 3600bk1 [0, 0, 0, 5325, 459250] [2] 9216 $$\Gamma_0(N)$$-optimal
3600.f6 3600bk2 [0, 0, 0, -66675, 6003250] [2, 2] 18432
3600.f7 3600bk3 [0, 0, 0, -48675, -13526750] [2] 27648
3600.f5 3600bk4 [0, 0, 0, -246675, -40616750] [2] 36864
3600.f4 3600bk5 [0, 0, 0, -1038675, 407439250] [2] 36864
3600.f3 3600bk6 [0, 0, 0, -1200675, -505430750] [2, 2] 55296
3600.f1 3600bk7 [0, 0, 0, -19200675, -32383430750] [2] 110592
3600.f2 3600bk8 [0, 0, 0, -1632675, -109286750] [2] 110592

## Rank

sage: E.rank()

The elliptic curves in class 3600bk have rank $$1$$.

## Modular form3600.2.a.f

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.