# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("980.h1")

sage: E.isogeny_class()

## Elliptic curves in class 980.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
980.h1 980g3 [0, -1, 0, -2025, 35750]  540
980.h2 980g4 [0, -1, 0, -1780, 44472]  1080
980.h3 980g1 [0, -1, 0, -65, -118]  180 $$\Gamma_0(N)$$-optimal
980.h4 980g2 [0, -1, 0, 180, -1000]  360

## Rank

sage: E.rank()

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

## 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. 