Elliptic curve isogeny class 19.1-a over number field 4.4.17725.1

• Base field: 4.4.17725.1
• Label: 4.4.17725.1-19.1-a
• Conductor: 19.1
• Rank bounds: 0...1

Base field 4.4.17725.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 12 x^{2} + 13 x + 41 \); class number \(1\).

Elliptic curves in class 19.1-a over 4.4.17725.1

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{2} - 7\) , \( 0\) , \( a^{3} - 8 a - 7\) , \( 2 a^{3} - 13 a - 6\) , \( 5 a^{3} + 6 a^{2} - 40 a - 63\bigr] \)
19.1-a2	\( \bigl[a^{2} - 7\) , \( 0\) , \( a^{3} - 8 a - 7\) , \( -23 a^{3} - 20 a^{2} + 172 a + 219\) , \( -190 a^{3} - 208 a^{2} + 1436 a + 2087\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph