Elliptic curve isogeny class 35.1-a over number field 3.3.1825.1

• Base field: 3.3.1825.1
• Label: 3.3.1825.1-35.1-a
• Conductor: 35.1
• Rank: \( 1 \)

Base field 3.3.1825.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 8 x + 7 \); class number \(1\).

Elliptic curves in class 35.1-a over 3.3.1825.1

Isogeny class 35.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
35.1-a1	\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 17 a - 68\) , \( -33 a^{2} + 24 a + 124\bigr] \)
35.1-a2	\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -5 a^{2} + 17 a - 8\) , \( -17 a^{2} + 67 a - 52\bigr] \)
35.1-a3	\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 2 a + 2\) , \( a^{2} + 2 a - 9\bigr] \)
35.1-a4	\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -8 a + 7\) , \( -8 a^{2} - 11 a + 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph