# Properties

 Label 6930.g Number of curves $2$ Conductor $6930$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6930.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.g1 6930j1 $$[1, -1, 0, -44955, 3679825]$$ $$13782741913468081/701662500$$ $$511511962500$$ $$$$ $$23040$$ $$1.3167$$ $$\Gamma_0(N)$$-optimal
6930.g2 6930j2 $$[1, -1, 0, -42525, 4093411]$$ $$-11666347147400401/3126621093750$$ $$-2279306777343750$$ $$$$ $$46080$$ $$1.6633$$

## Rank

sage: E.rank()

The elliptic curves in class 6930.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6930.g do not have complex multiplication.

## Modular form6930.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + q^{11} + 4 q^{13} - q^{14} + q^{16} + 4 q^{17} + 8 q^{19} + O(q^{20})$$

## 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. 