Elliptic curve isogeny class 175.2-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-175.2-a
• Conductor: 175.2
• Rank: \( 0 \)

Base field 3.3.733.1

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

Elliptic curves in class 175.2-a over 3.3.733.1

Isogeny class 175.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
175.2-a1	\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( 33 a^{2} + a - 225\) , \( -218 a^{2} - 51 a + 1450\bigr] \)
175.2-a2	\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( -2 a^{2} + a + 15\) , \( a^{2} + a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph