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

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-242.1-a
• 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-a over \(\Q(\sqrt{14}) \)

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

Curve label	Weierstrass Coefficients
242.1-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -10 a + 29\) , \( -9 a + 29\bigr] \)
242.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 30 a - 121\) , \( 147 a - 555\bigr] \)
242.1-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 425 a - 1601\) , \( 10255 a - 38379\bigr] \)
242.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 275 a - 1041\) , \( -4217 a + 15773\bigr] \)

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