Elliptic curve isogeny class 27.1-a over number field \(\Q(\sqrt{3}, \sqrt{7})\)

• Base field: \(\Q(\sqrt{3}, \sqrt{7})\)
• Label: 4.4.7056.1-27.1-a
• Conductor: 27.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}, \sqrt{7})\)

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 1 \); class number \(1\).

Elliptic curves in class 27.1-a over \(\Q(\sqrt{3}, \sqrt{7})\)

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -3 a^{3} + 8 a^{2} + 23 a - 16\) , \( 32 a^{3} + 92 a^{2} + 29 a - 42\bigr] \)
27.1-a2	\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 11 a^{3} + 4 a^{2} - 56 a - 22\) , \( 78 a^{3} + 35 a^{2} - 373 a - 169\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph