Elliptic curve isogeny class 8.3-a over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-8.3-a
• Conductor: 8.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{113}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 28 \); class number \(1\).

Elliptic curves in class 8.3-a over \(\Q(\sqrt{113}) \)

Isogeny class 8.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
8.3-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -a + 18\) , \( -a + 15\bigr] \)
8.3-a2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 485 a - 2806\) , \( 13245 a - 76988\bigr] \)
8.3-a3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 7650 a - 44471\) , \( 846103 a - 4920118\bigr] \)
8.3-a4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -140228 a - 675213\) , \( 65294067 a + 314395690\bigr] \)

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