# Properties

 Label 6930.i Number of curves $2$ Conductor $6930$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 6930.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.i1 6930c1 $$[1, -1, 0, -2094, -33580]$$ $$51603494067/4336640$$ $$85358085120$$ $$[2]$$ $$7680$$ $$0.83928$$ $$\Gamma_0(N)$$-optimal
6930.i2 6930c2 $$[1, -1, 0, 2226, -157132]$$ $$61958108493/573927200$$ $$-11296609077600$$ $$[2]$$ $$15360$$ $$1.1859$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6930.2.a.i

sage: E.q_eigenform(10)

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

## 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.