Elliptic curve isogeny class 10.2-a over number field 3.3.940.1

• Base field: 3.3.940.1
• Label: 3.3.940.1-10.2-a
• Conductor: 10.2
• Rank: \( 1 \)

Base field 3.3.940.1

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

Elliptic curves in class 10.2-a over 3.3.940.1

Isogeny class 10.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.2-a1	\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( 13396 a^{2} - 30712 a - 23365\) , \( -767129 a^{2} + 1758563 a + 1338569\bigr] \)
10.2-a2	\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 4\) , \( -27 a^{2} + 62 a + 49\) , \( -75 a^{2} + 171 a + 127\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph