Elliptic curve isogeny class 4.1-d over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-4.1-d
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-d over \(\Q(\sqrt{113}) \)

Isogeny class 4.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4.1-d1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 27992 a - 162776\) , \( -5873416 a + 34154342\bigr] \)
4.1-d2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 74632 a - 433991\) , \( 17928072 a - 104253046\bigr] \)
4.1-d3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -74632 a - 359359\) , \( -17928072 a - 86324974\bigr] \)
4.1-d4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -27992 a - 134784\) , \( 5873416 a + 28280926\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph