# Properties

 Label 7744m Number of curves $2$ Conductor $7744$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 7744m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7744.c2 7744m1 [0, 1, 0, -161, -3137] [] 3072 $$\Gamma_0(N)$$-optimal
7744.c1 7744m2 [0, 1, 0, -232481, 43068991] [] 33792

## Rank

sage: E.rank()

The elliptic curves in class 7744m have rank $$2$$.

## Complex multiplication

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

## Modular form7744.2.a.m

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. 