# Properties

 Label 720.b Number of curves $4$ Conductor $720$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 720.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.b1 720f4 [0, 0, 0, -3483, 20682]  1152
720.b2 720f2 [0, 0, 0, -2043, -35542]  384
720.b3 720f1 [0, 0, 0, -123, -598]  192 $$\Gamma_0(N)$$-optimal
720.b4 720f3 [0, 0, 0, 837, 2538]  576

## Rank

sage: E.rank()

The elliptic curves in class 720.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 720.b do not have complex multiplication.

## Modular form720.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{7} + 6q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 