Elliptic curve isogeny class 512.1-b over number field 3.3.361.1

• Base field: 3.3.361.1
• Label: 3.3.361.1-512.1-b
• Conductor: 512.1
• Rank: \( 1 \)

Base field 3.3.361.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 6 x + 7 \); class number \(1\).

Elliptic curves in class 512.1-b over 3.3.361.1

Isogeny class 512.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
512.1-b1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2457 a^{2} + 497 a - 14194\) , \( -95805 a^{2} - 20965 a + 549589\bigr] \)
512.1-b2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 112 a^{2} - 18 a - 769\) , \( -1208 a^{2} + 27 a + 7679\bigr] \)
512.1-b3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 112 a^{2} - 23 a - 759\) , \( -1232 a^{2} + 22 a + 7799\bigr] \)
512.1-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -558 a^{2} - 883 a + 1296\) , \( 15339 a^{2} + 21339 a - 42910\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph