# Properties

 Label 3600bh Number of curves 4 Conductor 3600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3600.be1")

sage: E.isogeny_class()

## Elliptic curves in class 3600bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.be3 3600bh1 [0, 0, 0, -300, 1375] [2] 1152 $$\Gamma_0(N)$$-optimal
3600.be4 3600bh2 [0, 0, 0, 825, 9250] [2] 2304
3600.be1 3600bh3 [0, 0, 0, -9300, -345125] [2] 3456
3600.be2 3600bh4 [0, 0, 0, -8175, -431750] [2] 6912

## Rank

sage: E.rank()

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

## Modular form3600.2.a.be

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.