# Properties

 Label 5610.bc Number of curves 6 Conductor 5610 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.bc1 5610bb5 [1, 1, 1, -292140, -60890853] [2] 49152
5610.bc2 5610bb3 [1, 1, 1, -19890, -778053] [2, 2] 24576
5610.bc3 5610bb2 [1, 1, 1, -7390, 231947] [2, 4] 12288
5610.bc4 5610bb1 [1, 1, 1, -7310, 237515] [4] 6144 $$\Gamma_0(N)$$-optimal
5610.bc5 5610bb4 [1, 1, 1, 3830, 887195] [4] 24576
5610.bc6 5610bb6 [1, 1, 1, 52360, -5055253] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 5610.bc have rank $$0$$.

## Modular form5610.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 6q^{13} - q^{15} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.