Elliptic curve isogeny class 100.1-b over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-100.1-b
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -120441 a - 524988\) , \( -72515124 a - 316086098\bigr] \)
100.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 12159 a + 53002\) , \( 1587234 a + 6918592\bigr] \)
100.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-b4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph