# Properties

 Label 1980b Number of curves 4 Conductor 1980 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1980.a1")

sage: E.isogeny_class()

## Elliptic curves in class 1980b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1980.a4 1980b1 [0, 0, 0, -408, -3107]  864 $$\Gamma_0(N)$$-optimal
1980.a3 1980b2 [0, 0, 0, -903, 5902]  1728
1980.a2 1980b3 [0, 0, 0, -4008, 96433]  2592
1980.a1 1980b4 [0, 0, 0, -63903, 6217702]  5184

## Rank

sage: E.rank()

The elliptic curves in class 1980b have rank $$0$$.

## Modular form1980.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + q^{11} - 4q^{13} - 4q^{19} + O(q^{20})$$

## 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. 