Elliptic curve isogeny class 2.1-b over number field \(\Q(\sqrt{114}) \)

• Base field: \(\Q(\sqrt{114}) \)
• Label: 2.2.456.1-2.1-b
• Conductor: 2.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{114}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 114 \); class number \(2\).

Elliptic curves in class 2.1-b over \(\Q(\sqrt{114}) \)

Isogeny class 2.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2.1-b1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 590112 a - 6300672\) , \( -806437026 a + 8610391232\bigr] \)
2.1-b2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 2322 a - 24792\) , \( -194400 a + 2075624\bigr] \)
2.1-b3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 36882 a - 393792\) , \( -12607488 a + 134611136\bigr] \)
2.1-b4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 36612 a - 390912\) , \( -12800862 a + 136675808\bigr] \)

Rank

Rank: \( 0 \)

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