# Properties

 Label 77616gn Number of curves 4 Conductor 77616 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("77616.bz1")

sage: E.isogeny_class()

## Elliptic curves in class 77616gn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.bz3 77616gn1 [0, 0, 0, -46011, 3766826] [2] 221184 $$\Gamma_0(N)$$-optimal
77616.bz2 77616gn2 [0, 0, 0, -81291, -2802310] [2, 2] 442368
77616.bz4 77616gn3 [0, 0, 0, 306789, -21818230] [2] 884736
77616.bz1 77616gn4 [0, 0, 0, -1033851, -404211094] [2] 884736

## Rank

sage: E.rank()

The elliptic curves in class 77616gn have rank $$1$$.

## Modular form 77616.2.a.bz

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.