# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("bc1")

E.isogeny_class()

## Elliptic curves in class 5610.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bc1 5610bb5 $$[1, 1, 1, -292140, -60890853]$$ $$2757381641970898311361/379829992662450$$ $$379829992662450$$ $$[2]$$ $$49152$$ $$1.8152$$
5610.bc2 5610bb3 $$[1, 1, 1, -19890, -778053]$$ $$870220733067747361/247623269602500$$ $$247623269602500$$ $$[2, 2]$$ $$24576$$ $$1.4686$$
5610.bc3 5610bb2 $$[1, 1, 1, -7390, 231947]$$ $$44633474953947361/1967006250000$$ $$1967006250000$$ $$[2, 4]$$ $$12288$$ $$1.1220$$
5610.bc4 5610bb1 $$[1, 1, 1, -7310, 237515]$$ $$43199583152847841/89760000$$ $$89760000$$ $$[4]$$ $$6144$$ $$0.77545$$ $$\Gamma_0(N)$$-optimal
5610.bc5 5610bb4 $$[1, 1, 1, 3830, 887195]$$ $$6213165856218719/342407226562500$$ $$-342407226562500$$ $$[4]$$ $$24576$$ $$1.4686$$
5610.bc6 5610bb6 $$[1, 1, 1, 52360, -5055253]$$ $$15875306080318016639/20322604533582450$$ $$-20322604533582450$$ $$[2]$$ $$49152$$ $$1.8152$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 5610.bc do not have complex multiplication.

## Modular form5610.2.a.bc

sage: E.q_eigenform(10)

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

## 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.