Elliptic curve isogeny class 8.4-a over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-8.4-a
• Conductor: 8.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 8.4-a over \(\Q(\sqrt{113}) \)

Isogeny class 8.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
8.4-a1	\( \bigl[a\) , \( -a\) , \( a\) , \( 140226 a - 815439\) , \( -65294068 a + 379689758\bigr] \)
8.4-a2	\( \bigl[a\) , \( 0\) , \( 0\) , \( a + 17\) , \( a + 14\bigr] \)
8.4-a3	\( \bigl[a\) , \( -a\) , \( a\) , \( -487 a - 2319\) , \( -13246 a - 63742\bigr] \)
8.4-a4	\( \bigl[a\) , \( -a\) , \( a\) , \( -7652 a - 36819\) , \( -846104 a - 4074014\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph