Elliptic curve isogeny class 6272.4-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6272.4-d
• Conductor: 6272.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 6272.4-d over \(\Q(\sqrt{-7}) \)

Isogeny class 6272.4-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
6272.4-d1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 58 a - 28\bigr] \)
6272.4-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 28 a + 40\) , \( 84 a - 216\bigr] \)
6272.4-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -28 a + 68\) , \( 84 a + 132\bigr] \)
6272.4-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 282\) , \( 1458 a - 588\bigr] \)

Rank

Rank: \( 1 \)

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