# Properties

 Label 76230.bk Number of curves $4$ Conductor $76230$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76230.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 76230.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.bk1 76230i3 [1, -1, 0, -114549, 14932385] [2] 414720
76230.bk2 76230i4 [1, -1, 0, -81879, 23603003] [2] 829440
76230.bk3 76230i1 [1, -1, 0, -5649, -141795] [2] 138240 $$\Gamma_0(N)$$-optimal
76230.bk4 76230i2 [1, -1, 0, 8871, -760347] [2] 276480

## Rank

sage: E.rank()

The elliptic curves in class 76230.bk have rank $$1$$.

## Modular form 76230.2.a.bk

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 2q^{13} + q^{14} + q^{16} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.