Elliptic curve isogeny class 14.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-14.1-b
• Conductor: 14.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 14.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 14.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
14.1-b1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 20462 a - 76559\) , \( -3121544 a + 11679749\bigr] \)
14.1-b2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 62 a - 229\) , \( 960 a - 3591\bigr] \)
14.1-b3	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -538 a + 2016\) , \( -21216 a + 79384\bigr] \)
14.1-b4	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4262 a - 15944\) , \( -246560 a + 922544\bigr] \)
14.1-b5	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1262 a - 4719\) , \( 45312 a - 169541\bigr] \)
14.1-b6	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 327662 a - 1225999\) , \( -197976456 a + 740760069\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph