Elliptic curve isogeny class 242.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-242.1-b
• Conductor: 242.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 242.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 242.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
242.1-b1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 8 a + 29\) , \( 8 a + 29\bigr] \)
242.1-b2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -32 a - 121\) , \( -148 a - 555\bigr] \)
242.1-b3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -277 a - 1041\) , \( 4216 a + 15773\bigr] \)
242.1-b4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -427 a - 1601\) , \( -10256 a - 38379\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph