# Properties

 Label 720.d Number of curves $6$ Conductor $720$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 720.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.d1 720c5 [0, 0, 0, -28803, -1881502]  1024
720.d2 720c3 [0, 0, 0, -1803, -29302] [2, 2] 512
720.d3 720c6 [0, 0, 0, -723, -64078]  1024
720.d4 720c2 [0, 0, 0, -183, 182] [2, 2] 256
720.d5 720c1 [0, 0, 0, -138, 623]  128 $$\Gamma_0(N)$$-optimal
720.d6 720c4 [0, 0, 0, 717, 1442]  512

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form720.2.a.d

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 