Elliptic curve isogeny class 8.1-c over number field 3.3.1849.1

• Base field: 3.3.1849.1
• Label: 3.3.1849.1-8.1-c
• Conductor: 8.1
• Rank: \( 0 \)

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 8.1-c over 3.3.1849.1

Isogeny class 8.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.1-c1	\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( \frac{219}{2} a^{2} - \frac{355}{2} a - 1425\) , \( -140149 a^{2} + 226349 a + 1822858\bigr] \)
8.1-c2	\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -988 a^{2} + 1595 a + 12850\) , \( 3783807 a^{2} - 6111121 a - 49214528\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph