# Properties

 Label 77b Number of curves 3 Conductor 77 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("77.b1")

sage: E.isogeny_class()

## Elliptic curves in class 77b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77.b2 77b1 [0, 1, 1, -49, 600]  20 $$\Gamma_0(N)$$-optimal
77.b3 77b2 [0, 1, 1, 441, -15815] [] 60
77.b1 77b3 [0, 1, 1, -89, 295]  60

## Rank

sage: E.rank()

The elliptic curves in class 77b have rank $$0$$.

## Modular form77.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + 3q^{5} + q^{7} - 2q^{9} - q^{11} - 2q^{12} - 4q^{13} + 3q^{15} + 4q^{16} - 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 