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

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-4.1-a
• Conductor: 4.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 76 a - 435\) , \( -300 a + 1741\bigr] \)
4.1-a2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -186564 a - 898307\) , \( -91146540 a - 438877227\bigr] \)
4.1-a3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 2861 a - 16630\) , \( 197859 a - 1150568\bigr] \)
4.1-a4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 2260547 a - 13145249\) , \( 5564451284 a - 32357689912\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph