# Properties

 Label 7744bc Number of curves $2$ Conductor $7744$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 7744bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7744.be2 7744bc1 [0, -1, 0, -1921, 33057] [] 3072 $$\Gamma_0(N)$$-optimal
7744.be1 7744bc2 [0, -1, 0, -19521, -4097311] [] 33792

## Rank

sage: E.rank()

The elliptic curves in class 7744bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7744bc do not have complex multiplication.

## Modular form7744.2.a.bc

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} - 2q^{7} + q^{9} + q^{13} - 2q^{15} + 5q^{17} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.