Elliptic curve isogeny class 19.3-d over number field 3.3.1489.1

• Base field: 3.3.1489.1
• Label: 3.3.1489.1-19.3-d
• Conductor: 19.3
• Rank: \( 1 \)

Base field 3.3.1489.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 10 x - 7 \); class number \(1\).

Elliptic curves in class 19.3-d over 3.3.1489.1

Isogeny class 19.3-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
19.3-d1	\( \bigl[0\) , \( a^{2} - 3 a - 7\) , \( a\) , \( -a^{2} + 3 a + 8\) , \( -a - 3\bigr] \)
19.3-d2	\( \bigl[0\) , \( a^{2} - 3 a - 7\) , \( a\) , \( -11 a^{2} + 33 a + 38\) , \( -53 a^{2} + 173 a + 179\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph