Elliptic curve isogeny class 13.3-b over number field 3.3.1257.1

• Base field: 3.3.1257.1
• Label: 3.3.1257.1-13.3-b
• Conductor: 13.3
• Rank: \( 1 \)

Base field 3.3.1257.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 8 x + 9 \); class number \(1\).

Elliptic curves in class 13.3-b over 3.3.1257.1

Isogeny class 13.3-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
13.3-b1	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 5\) , \( -2309 a^{2} - 3982 a + 7630\) , \( 128122 a^{2} + 220876 a - 423320\bigr] \)
13.3-b2	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 5\) , \( -187059 a^{2} - 322482 a + 618050\) , \( 92545433 a^{2} + 159544299 a - 305771736\bigr] \)
13.3-b3	\( \bigl[0\) , \( -a^{2} + a + 7\) , \( a^{2} - 6\) , \( -10 a^{2} + 4 a + 24\) , \( 5 a^{2} - 78 a + 89\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph