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

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-4.1-b
• Conductor: 4.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 3166 a - 18410\) , \( -216410 a + 1258440\bigr] \)
4.1-b2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -3166 a - 15244\) , \( 216410 a + 1042030\bigr] \)
4.1-b3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -34016 a - 163789\) , \( -7810456 a - 37607915\bigr] \)
4.1-b4	\( \bigl[1\) , \( 1\) , \( 0\) , \( 34016 a - 197805\) , \( 7810456 a - 45418371\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph