# Properties

 Label 76230.fg Number of curves $4$ Conductor $76230$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fg1")

sage: E.isogeny_class()

## Elliptic curves in class 76230.fg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.fg1 76230fe4 [1, -1, 1, -291512, -60504551] [2] 655360
76230.fg2 76230fe3 [1, -1, 1, -95492, 10637641] [2] 655360
76230.fg3 76230fe2 [1, -1, 1, -19262, -827351] [2, 2] 327680
76230.fg4 76230fe1 [1, -1, 1, 2518, -78119] [2] 163840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 76230.fg do not have complex multiplication.

## Modular form 76230.2.a.fg

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 6q^{13} + q^{14} + q^{16} + 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.