# Properties

 Label 76230.ek Number of curves 4 Conductor 76230 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76230.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 76230.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.ek1 76230en4 [1, -1, 1, -28440347, -56716844929]  9953280
76230.ek2 76230en2 [1, -1, 1, -3894287, 2932642199]  3317760
76230.ek3 76230en1 [1, -1, 1, -61007, 112881431]  1658880 $$\Gamma_0(N)$$-optimal
76230.ek4 76230en3 [1, -1, 1, 548833, -3040479241]  4976640

## Rank

sage: E.rank()

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

## Modular form 76230.2.a.ek

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 