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

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-44.1-b
• Conductor: 44.1
• Rank: \( 2 \)

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

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

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

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

Curve label	Weierstrass Coefficients
44.1-b1	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -1160 a - 3847\) , \( 39003 a + 129357\bigr] \)
44.1-b2	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 40 a + 133\) , \( 301 a + 997\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph