# Properties

 Label 73920n Number of curves $6$ Conductor $73920$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 73920n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.bx6 73920n1 [0, -1, 0, 2239, -11843775] [2] 491520 $$\Gamma_0(N)$$-optimal
73920.bx5 73920n2 [0, -1, 0, -766081, -253249919] [2, 2] 983040
73920.bx4 73920n3 [0, -1, 0, -1628481, 422354241] [2] 1966080
73920.bx2 73920n4 [0, -1, 0, -12196801, -16391140415] [2, 2] 1966080
73920.bx3 73920n5 [0, -1, 0, -12136321, -16561802879] [2] 3932160
73920.bx1 73920n6 [0, -1, 0, -195148801, -1049228361215] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 73920n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 73920n do not have complex multiplication.

## Modular form 73920.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.