Elliptic curve isogeny class 20.1-b over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-20.1-b
• Conductor: 20.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 20.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
20.1-b1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -10254 a - 44701\) , \( 1141271 a + 4974682\bigr] \)
20.1-b2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -84 a - 371\) , \( 2293 a + 9992\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph