Elliptic curve isogeny class 112.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-112.1-b
• Conductor: 112.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 112.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 112.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
112.1-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -8820 a - 32996\) , \( -939060 a - 3513640\bigr] \)
112.1-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -30 a + 119\) , \( 854 a - 3192\bigr] \)
112.1-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 1770 a - 6616\) , \( -59376 a + 222168\bigr] \)
112.1-b4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -570 a - 2126\) , \( -14340 a - 53652\bigr] \)
112.1-b5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 8970 a - 33556\) , \( 907960 a - 3397272\bigr] \)
112.1-b6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 8820 a - 32996\) , \( 939060 a - 3513640\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph