# Properties

 Label 120b Number of curves 4 Conductor 120 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("120.a1")

sage: E.isogeny_class()

## Elliptic curves in class 120b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
120.a4 120b1 [0, 1, 0, 4, 0]  8 $$\Gamma_0(N)$$-optimal
120.a3 120b2 [0, 1, 0, -16, -16] [2, 2] 16
120.a1 120b3 [0, 1, 0, -216, -1296]  32
120.a2 120b4 [0, 1, 0, -136, 560]  32

## Rank

sage: E.rank()

The elliptic curves in class 120b have rank $$0$$.

## Modular form120.2.a.a

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 4q^{7} + q^{9} - 6q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 