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

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-10.1-b
• 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-b over \(\Q(\sqrt{11}) \)

Isogeny class 10.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -23541 a - 78106\) , \( -3623860 a - 12019033\bigr] \)
10.1-b2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 14 a + 49\) , \( 2175 a + 7212\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph