Elliptic curve isogeny class 44.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-44.1-a
• Conductor: 44.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 44.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 44.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
44.1-a1	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -1160 a - 3847\) , \( -39004 a - 129363\bigr] \)
44.1-a2	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 40 a + 133\) , \( -302 a - 1003\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph