# Properties

 Label 76230i 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 76230i

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

The elliptic curves in class 76230i 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 Cremona 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 Cremona labels. 