Elliptic curve isogeny class 23.1-d over number field 4.4.9792.1

• Base field: 4.4.9792.1
• Label: 4.4.9792.1-23.1-d
• Conductor: 23.1
• Rank: \( 1 \)

Base field 4.4.9792.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7 \); class number \(1\).

Elliptic curves in class 23.1-d over 4.4.9792.1

Isogeny class 23.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
23.1-d1	\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 29 a^{3} - 102 a^{2} - 49 a + 134\) , \( -75 a^{3} + 263 a^{2} + 130 a - 348\bigr] \)
23.1-d2	\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 5 a + 11\) , \( -a^{3} + 4 a^{2} + a - 7\) , \( 4 a^{3} - 6 a^{2} - 27 a - 16\) , \( -7 a^{3} + 4 a^{2} + 62 a + 57\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph