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

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

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

Curve label	Weierstrass Coefficients
30492.5-h1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 46 a - 281\) , \( -476 a + 1629\bigr] \)
30492.5-h2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 56 a - 11\) , \( 108 a - 11\bigr] \)
30492.5-h3	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -204 a - 31\) , \( 768 a + 473\bigr] \)
30492.5-h4	\( \bigl[1\) , \( -a\) , \( 1\) , \( -51 a + 172\) , \( -519 a - 268\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph