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

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-14.1-c
• Conductor: 14.1
• Rank: \( 0 \)

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

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

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

Isogeny class 14.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
14.1-c1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 67 a - 393\) , \( -359 a + 2076\bigr] \)
14.1-c2	\( \bigl[1\) , \( a\) , \( 1\) , \( 794947 a - 4622663\) , \( -890320822 a + 5177280498\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph