Elliptic curve isogeny class 1792.1-bl over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1792.1-bl
• Conductor: 1792.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

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

Elliptic curves in class 1792.1-bl over \(\Q(\sqrt{21}) \)

Isogeny class 1792.1-bl contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1792.1-bl1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 4\) , \( 4 a + 7\bigr] \)
1792.1-bl2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -17 a - 154\) , \( 256 a - 70\bigr] \)
1792.1-bl3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -37 a - 74\) , \( 200 a + 350\bigr] \)
1792.1-bl4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -617 a - 1114\) , \( 12688 a + 22722\bigr] \)

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