Elliptic curve isogeny class 14.1-f over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-14.1-f
• Conductor: 14.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 14.1-f over \(\Q(\sqrt{113}) \)

Isogeny class 14.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14.1-f1	\( \bigl[1\) , \( 1\) , \( 1\) , \( 1898040 a + 9139201\) , \( 41942564345 a + 201956505201\bigr] \)
14.1-f2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -13559 a - 65281\) , \( -1332816 a - 6417625\bigr] \)
14.1-f3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -5274 a - 25381\) , \( 472335 a + 2274331\bigr] \)
14.1-f4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 32 a - 251\) , \( 319 a - 1659\bigr] \)

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