# Properties

 Label 980.h Number of curves $4$ Conductor $980$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 980.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
980.h1 980g3 $$[0, -1, 0, -2025, 35750]$$ $$488095744/125$$ $$235298000$$ $$$$ $$540$$ $$0.59231$$
980.h2 980g4 $$[0, -1, 0, -1780, 44472]$$ $$-20720464/15625$$ $$-470596000000$$ $$$$ $$1080$$ $$0.93888$$
980.h3 980g1 $$[0, -1, 0, -65, -118]$$ $$16384/5$$ $$9411920$$ $$$$ $$180$$ $$0.043005$$ $$\Gamma_0(N)$$-optimal
980.h4 980g2 $$[0, -1, 0, 180, -1000]$$ $$21296/25$$ $$-752953600$$ $$$$ $$360$$ $$0.38958$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form980.2.a.h

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + q^{9} - 2q^{13} + 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 