# Properties

 Label 115600bz Number of curves 4 Conductor 115600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("115600.dc1")

sage: E.isogeny_class()

## Elliptic curves in class 115600bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
115600.dc4 115600bz1 [0, -1, 0, -349208, -49059088] [2] 1990656 $$\Gamma_0(N)$$-optimal
115600.dc3 115600bz2 [0, -1, 0, -4973208, -4266147088] [2] 3981312
115600.dc2 115600bz3 [0, -1, 0, -11909208, 15820508912] [2] 5971968
115600.dc1 115600bz4 [0, -1, 0, -13065208, 12565212912] [2] 11943936

## Rank

sage: E.rank()

The elliptic curves in class 115600bz have rank $$0$$.

## Modular form 115600.2.a.dc

sage: E.q_eigenform(10)

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

## 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.