# Properties

 Label 77616fk Number of curves 6 Conductor 77616 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("77616.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 77616fk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.bf4 77616fk1 [0, 0, 0, -240051, -45254734] [2] 491520 $$\Gamma_0(N)$$-optimal
77616.bf3 77616fk2 [0, 0, 0, -275331, -31079230] [2, 2] 983040
77616.bf6 77616fk3 [0, 0, 0, 888909, -225041614] [2] 1966080
77616.bf2 77616fk4 [0, 0, 0, -2004051, 1070115410] [2, 2] 1966080
77616.bf5 77616fk5 [0, 0, 0, 218589, 3313648226] [2] 3932160
77616.bf1 77616fk6 [0, 0, 0, -31886211, 69303039554] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 77616fk have rank $$0$$.

## Modular form 77616.2.a.bf

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{11} - 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.