# Properties

 Label 73920.bv Number of curves $6$ Conductor $73920$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("73920.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 73920.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.bv1 73920ew6 [0, -1, 0, -848001, 300836385] [2] 1048576
73920.bv2 73920ew4 [0, -1, 0, -56001, 4153185] [2, 2] 524288
73920.bv3 73920ew2 [0, -1, 0, -17281, -810719] [2, 2] 262144
73920.bv4 73920ew1 [0, -1, 0, -16961, -844575] [2] 131072 $$\Gamma_0(N)$$-optimal
73920.bv5 73920ew3 [0, -1, 0, 16319, -3612959] [2] 524288
73920.bv6 73920ew5 [0, -1, 0, 116479, 24540321] [2] 1048576

## Rank

sage: E.rank()

The elliptic curves in class 73920.bv have rank $$2$$.

## Modular form 73920.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.