Elliptic curve isogeny class 304.1-e over number field 3.3.148.1

• Base field: 3.3.148.1
• Label: 3.3.148.1-304.1-e
• Conductor: 304.1
• Rank: \( 1 \)

Base field 3.3.148.1

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

Elliptic curves in class 304.1-e over 3.3.148.1

Isogeny class 304.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
304.1-e1	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{2} - 1\) , \( -117 a^{2} - 136 a + 54\) , \( -1541 a^{2} - 1803 a + 710\bigr] \)
304.1-e2	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{2} - 1\) , \( -287 a^{2} - 316 a + 124\) , \( 2389 a^{2} + 2745 a - 1088\bigr] \)
304.1-e3	\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( 19 a^{2} - 59\) , \( 51 a^{2} - 24 a - 128\bigr] \)
304.1-e4	\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( -a^{2} + 1\) , \( -a^{2}\bigr] \)

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