Elliptic curve isogeny class 10.2-d over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-10.2-d
• Conductor: 10.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 10.2-d over \(\Q(\sqrt{11}) \)

Isogeny class 10.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
10.2-d1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 10 a - 31\) , \( 24 a - 79\bigr] \)
10.2-d2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -70 a + 234\) , \( -24 a + 80\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph