Elliptic curve isogeny class 10.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-10.1-a
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 10.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
10.1-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -8 a - 32\) , \( 15 a + 47\bigr] \)
10.1-a2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 72 a + 233\) , \( 47 a + 153\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph