# Properties

 Label 720j Number of curves 8 Conductor 720 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("720.j1")

sage: E.isogeny_class()

## Elliptic curves in class 720j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.j8 720j1 [0, 0, 0, 213, 3674] [2] 384 $$\Gamma_0(N)$$-optimal
720.j6 720j2 [0, 0, 0, -2667, 48026] [2, 2] 768
720.j7 720j3 [0, 0, 0, -1947, -108214] [2] 1152
720.j5 720j4 [0, 0, 0, -9867, -324934] [2] 1536
720.j4 720j5 [0, 0, 0, -41547, 3259514] [4] 1536
720.j3 720j6 [0, 0, 0, -48027, -4043446] [2, 2] 2304
720.j1 720j7 [0, 0, 0, -768027, -259067446] [2] 4608
720.j2 720j8 [0, 0, 0, -65307, -874294] [4] 4608

## Rank

sage: E.rank()

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

## Modular form720.2.a.j

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.