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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-a
• Conductor: 30492.5
• Rank: \( 2 \)

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

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

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

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

Curve label	Weierstrass Coefficients
30492.5-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( -23\bigr] \)
30492.5-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -21 a - 14\) , \( -56 a - 14\bigr] \)
30492.5-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -105\) , \( -441\bigr] \)
30492.5-a4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 20 a - 35\) , \( 55 a - 70\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph