Elliptic curve isogeny class 8.6-a over number field 3.3.1849.1

• Base field: 3.3.1849.1
• Label: 3.3.1849.1-8.6-a
• Conductor: 8.6
• Rank: \( 1 \)

Base field 3.3.1849.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 14 x - 8 \); class number \(1\).

Elliptic curves in class 8.6-a over 3.3.1849.1

Isogeny class 8.6-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.6-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -\frac{61}{2} a^{2} - \frac{213}{2} a - 54\) , \( \frac{739}{2} a^{2} + \frac{2591}{2} a + 657\bigr] \)
8.6-a2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -\frac{163899532916557}{2} a^{2} - \frac{574190484982959}{2} a - 145581466969102\) , \( 3309113155990949483684 a^{2} + 11592841383320317551922 a + 5878546924977252334056\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph