# Properties

 Label 6776.g Number of curves $4$ Conductor $6776$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 6776.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6776.g1 6776c3 [0, 0, 0, -36179, -2648690] [2] 10240
6776.g2 6776c4 [0, 0, 0, -7139, 183678] [2] 10240
6776.g3 6776c2 [0, 0, 0, -2299, -39930] [2, 2] 5120
6776.g4 6776c1 [0, 0, 0, 121, -2662] [2] 2560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6776.g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6776.g do not have complex multiplication.

## Modular form6776.2.a.g

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 3q^{9} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.