# Properties

 Label 4600.g Number of curves $2$ Conductor $4600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 4600.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4600.g1 4600i2 $$[0, 0, 0, -875, 7750]$$ $$2315250/529$$ $$16928000000$$ $$[2]$$ $$3456$$ $$0.67517$$
4600.g2 4600i1 $$[0, 0, 0, 125, 750]$$ $$13500/23$$ $$-368000000$$ $$[2]$$ $$1728$$ $$0.32860$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4600.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4600.g do not have complex multiplication.

## Modular form4600.2.a.g

sage: E.q_eigenform(10)

$$q - 4 q^{7} - 3 q^{9} + 6 q^{11} + 2 q^{13} - 6 q^{17} - 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.