Elliptic curve isogeny class 14.4-c over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-14.4-c
• Conductor: 14.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 14.4-c over \(\Q(\sqrt{113}) \)

Isogeny class 14.4-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
14.4-c1	\( \bigl[1\) , \( 0\) , \( a\) , \( -68 a - 325\) , \( 358 a + 1718\bigr] \)
14.4-c2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -794947 a - 3827716\) , \( 890320822 a + 4286959676\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph