Elliptic curve isogeny class 2.1-a over number field 3.3.1101.1

• Base field: 3.3.1101.1
• Label: 3.3.1101.1-2.1-a
• Conductor: 2.1
• Rank: \( 1 \)

Base field 3.3.1101.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 9 x + 12 \); class number \(1\).

Elliptic curves in class 2.1-a over 3.3.1101.1

Isogeny class 2.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2.1-a1	\( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( 0\) , \( a^{2} + 6 a - 10\) , \( 8 a - 12\bigr] \)
2.1-a2	\( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( 0\) , \( -258049030 a^{2} - 435431820 a + 1152261988\) , \( 3966553778797 a^{2} + 6693161107945 a - 17711785781052\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph