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

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-10.1-c
• Conductor: 10.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
10.1-c1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -23543 a - 78105\) , \( 3600318 a + 11940924\bigr] \)
10.1-c2	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 12 a + 50\) , \( -2162 a - 7166\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph