# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1980d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1980.f4 1980d1 $$[0, 0, 0, 1968, 123469]$$ $$72268906496/606436875$$ $$-7073479710000$$ $$$$ $$2304$$ $$1.1470$$ $$\Gamma_0(N)$$-optimal
1980.f3 1980d2 $$[0, 0, 0, -28407, 1696894]$$ $$13584145739344/1195803675$$ $$223165665043200$$ $$$$ $$4608$$ $$1.4936$$
1980.f2 1980d3 $$[0, 0, 0, -140592, 20306401]$$ $$-26348629355659264/24169921875$$ $$-281917968750000$$ $$$$ $$6912$$ $$1.6963$$
1980.f1 1980d4 $$[0, 0, 0, -2249967, 1299009526]$$ $$6749703004355978704/5671875$$ $$1058508000000$$ $$$$ $$13824$$ $$2.0429$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1980d do not have complex multiplication.

## Modular form1980.2.a.d

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} - q^{11} + 2q^{13} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 