# Properties

 Label 120a Number of curves 6 Conductor 120 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("120.b1")

sage: E.isogeny_class()

## Elliptic curves in class 120a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
120.b5 120a1 [0, 1, 0, -15, 18] [4] 8 $$\Gamma_0(N)$$-optimal
120.b4 120a2 [0, 1, 0, -20, 0] [2, 4] 16
120.b2 120a3 [0, 1, 0, -200, -1152] [2, 2] 32
120.b6 120a4 [0, 1, 0, 80, 80] [4] 32
120.b1 120a5 [0, 1, 0, -3200, -70752] [2] 64
120.b3 120a6 [0, 1, 0, -80, -2400] [2] 64

## Rank

sage: E.rank()

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

## Modular form120.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 4q^{11} + 6q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.