Elliptic curve isogeny class 392.1-f over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-392.1-f
• Conductor: 392.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 392.1-f over \(\Q(\sqrt{11}) \)

Isogeny class 392.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
392.1-f1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 17 a + 55\) , \( -257 a - 854\bigr] \)
392.1-f2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -883 a - 2930\) , \( 18298 a + 60686\bigr] \)
392.1-f3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 288 a - 934\) , \( 4304 a - 14256\bigr] \)
392.1-f4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 4488 a - 14864\) , \( 294804 a - 977736\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph