# Properties

 Label 600.g Number of curves $2$ Conductor $600$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 600.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
600.g1 600h2 [0, 1, 0, -4208, -66912]  960
600.g2 600h1 [0, 1, 0, 792, -6912]  480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 600.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 600.g do not have complex multiplication.

## Modular form600.2.a.g

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} + 2q^{11} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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. 