# Properties

 Label 980.g Number of curves $2$ Conductor $980$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 980.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
980.g1 980a1 $$[0, 1, 0, -996, 11780]$$ $$-177953104/125$$ $$-76832000$$ $$$$ $$432$$ $$0.44939$$ $$\Gamma_0(N)$$-optimal
980.g2 980a2 $$[0, 1, 0, 964, 51764]$$ $$161017136/1953125$$ $$-1200500000000$$ $$[]$$ $$1296$$ $$0.99869$$

## Rank

sage: E.rank()

The elliptic curves in class 980.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 980.g do not have complex multiplication.

## Modular form980.2.a.g

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2 q^{9} + 6 q^{11} + 2 q^{13} - q^{15} - 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 