# Properties

 Label 77616ex Number of curves 4 Conductor 77616 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("77616.dq1")

sage: E.isogeny_class()

## Elliptic curves in class 77616ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.dq3 77616ex1 [0, 0, 0, -38955, -2791334] [2] 276480 $$\Gamma_0(N)$$-optimal
77616.dq4 77616ex2 [0, 0, 0, 31605, -11780678] [2] 552960
77616.dq1 77616ex3 [0, 0, 0, -568155, 164203018] [2] 829440
77616.dq2 77616ex4 [0, 0, 0, -285915, 327394186] [2] 1658880

## Rank

sage: E.rank()

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

## Modular form 77616.2.a.dq

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.