# Properties

 Label 76230dk Number of curves $6$ Conductor $76230$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76230.de1")

sage: E.isogeny_class()

## Elliptic curves in class 76230dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.de6 76230dk1 [1, -1, 1, 10867, -612939] [2] 327680 $$\Gamma_0(N)$$-optimal
76230.de5 76230dk2 [1, -1, 1, -76253, -6293163] [2, 2] 655360
76230.de4 76230dk3 [1, -1, 1, -402953, 93154317] [2] 1310720
76230.de2 76230dk4 [1, -1, 1, -1143473, -470320419] [2, 2] 1310720
76230.de3 76230dk5 [1, -1, 1, -1067243, -535786743] [2] 2621440
76230.de1 76230dk6 [1, -1, 1, -18295223, -30115405119] [2] 2621440

## Rank

sage: E.rank()

The elliptic curves in class 76230dk have rank $$0$$.

## Modular form 76230.2.a.de

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2q^{13} - q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.