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

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-14.1-a
• 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-a over \(\Q(\sqrt{113}) \)

Isogeny class 14.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.1-a1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -1886 a - 9086\) , \( -51323 a - 247128\bigr] \)
14.1-a2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -127126 a - 612126\) , \( -57375186 a - 276265708\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph