Elliptic curve isogeny class 12.2-d over number field 3.3.1509.1

• Base field: 3.3.1509.1
• Label: 3.3.1509.1-12.2-d
• Conductor: 12.2
• Rank: \( 1 \)

Base field 3.3.1509.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 4 \); class number \(1\).

Elliptic curves in class 12.2-d over 3.3.1509.1

Isogeny class 12.2-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
12.2-d1	\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 5\) , \( -21 a^{2} + 194 a - 94\) , \( 422 a^{2} - 1452 a + 679\bigr] \)
12.2-d2	\( \bigl[a\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -3 a^{2} - 5 a + 13\) , \( 3 a^{2} + 2 a - 9\bigr] \)
12.2-d3	\( \bigl[a\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -153 a^{2} - 300 a + 203\) , \( 2496 a^{2} + 4822 a - 3368\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph