# Properties

 Label 76230fa Number of curves 4 Conductor 76230 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76230.eu1")

sage: E.isogeny_class()

## Elliptic curves in class 76230fa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.eu3 76230fa1 [1, -1, 1, -545612, -134557761] [2] 1474560 $$\Gamma_0(N)$$-optimal
76230.eu2 76230fa2 [1, -1, 1, -2309792, 1217509791] [2, 2] 2949120
76230.eu4 76230fa3 [1, -1, 1, 3080758, 6051755031] [2] 5898240
76230.eu1 76230fa4 [1, -1, 1, -35927222, 82894417719] [2] 5898240

## Rank

sage: E.rank()

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

## Modular form 76230.2.a.eu

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.