Elliptic curve isogeny class 392.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-392.1-b
• Conductor: 392.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 392.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 392.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
392.1-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a + 10\) , \( 5 a + 8\bigr] \)
392.1-b2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a - 95\) , \( -170 a - 97\bigr] \)
392.1-b3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a - 25\) , \( 12 a - 27\bigr] \)
392.1-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a - 515\) , \( 1482 a - 517\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph