Elliptic curve isogeny class 30492.5-s over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-s
• Conductor: 30492.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 30492.5-s over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-s contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
30492.5-s1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 169 a - 122\) , \( -804 a - 191\bigr] \)
30492.5-s2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 19 a - 902\) , \( 546 a - 12803\bigr] \)
30492.5-s3	\( \bigl[1\) , \( a\) , \( a\) , \( -20 a - 882\) , \( -547 a - 12256\bigr] \)
30492.5-s4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -823\) , \( -11611\bigr] \)
30492.5-s5	\( \bigl[1\) , \( 0\) , \( 0\) , \( 77\) , \( 161\bigr] \)
30492.5-s6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -363\) , \( 1305\bigr] \)
30492.5-s7	\( \bigl[1\) , \( a\) , \( a\) , \( -170 a + 48\) , \( 803 a - 994\bigr] \)
30492.5-s8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -14133\) , \( -647829\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 12 & 6 & 2 & 4 & 4 & 12 \\ 3 & 1 & 4 & 2 & 6 & 12 & 12 & 4 \\ 12 & 4 & 1 & 2 & 6 & 12 & 3 & 4 \\ 6 & 2 & 2 & 1 & 3 & 6 & 6 & 2 \\ 2 & 6 & 6 & 3 & 1 & 2 & 2 & 6 \\ 4 & 12 & 12 & 6 & 2 & 1 & 4 & 3 \\ 4 & 12 & 3 & 6 & 2 & 4 & 1 & 12 \\ 12 & 4 & 4 & 2 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph