# Properties

 Label 6930.x Number of curves $4$ Conductor $6930$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.x1 6930bc4 $$[1, -1, 1, -188183, 31467871]$$ $$1010962818911303721/57392720$$ $$41839292880$$ $$$$ $$32768$$ $$1.5047$$
6930.x2 6930bc3 $$[1, -1, 1, -19703, -246113]$$ $$1160306142246441/634128110000$$ $$462279392190000$$ $$$$ $$32768$$ $$1.5047$$
6930.x3 6930bc2 $$[1, -1, 1, -11783, 492031]$$ $$248158561089321/1859334400$$ $$1355454777600$$ $$[2, 2]$$ $$16384$$ $$1.1581$$
6930.x4 6930bc1 $$[1, -1, 1, -263, 17407]$$ $$-2749884201/176619520$$ $$-128755630080$$ $$$$ $$8192$$ $$0.81155$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6930.x have rank $$1$$.

## Complex multiplication

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

## Modular form6930.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + q^{11} - 6q^{13} + q^{14} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 