# Properties

 Label 120a Number of curves $6$ Conductor $120$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 120a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
120.b5 120a1 $$[0, 1, 0, -15, 18]$$ $$24918016/45$$ $$720$$ $$$$ $$8$$ $$-0.55972$$ $$\Gamma_0(N)$$-optimal
120.b4 120a2 $$[0, 1, 0, -20, 0]$$ $$3631696/2025$$ $$518400$$ $$[2, 4]$$ $$16$$ $$-0.21315$$
120.b2 120a3 $$[0, 1, 0, -200, -1152]$$ $$868327204/5625$$ $$5760000$$ $$[2, 2]$$ $$32$$ $$0.13343$$
120.b6 120a4 $$[0, 1, 0, 80, 80]$$ $$54607676/32805$$ $$-33592320$$ $$$$ $$32$$ $$0.13343$$
120.b1 120a5 $$[0, 1, 0, -3200, -70752]$$ $$1770025017602/75$$ $$153600$$ $$$$ $$64$$ $$0.48000$$
120.b3 120a6 $$[0, 1, 0, -80, -2400]$$ $$-27995042/1171875$$ $$-2400000000$$ $$$$ $$64$$ $$0.48000$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 120a do not have complex multiplication.

## Modular form120.2.a.a

sage: E.q_eigenform(10)

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

## 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 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. 