Elliptic curve isogeny class 200.1-b over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-200.1-b
• Conductor: 200.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 200.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 200.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -43089 a + 187873\) , \( 19168276 a - 83552505\bigr] \)
200.1-b2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 23211 a - 101122\) , \( 3377115 a - 14720430\bigr] \)
200.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
200.1-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 354711 a - 1546097\) , \( 240006580 a - 1046164355\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph