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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-l
• 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-l over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30492.5-l1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 51 a + 121\) , \( 519 a - 787\bigr] \)
30492.5-l2	\( \bigl[1\) , \( -a\) , \( 0\) , \( 204 a - 235\) , \( -768 a + 1241\bigr] \)
30492.5-l3	\( \bigl[1\) , \( -a\) , \( 0\) , \( -56 a + 45\) , \( -108 a + 97\bigr] \)
30492.5-l4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -44 a - 237\) , \( 521 a + 1389\bigr] \)

Rank

Rank: \( 1 \)

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