Elliptic curve isogeny class 30.2-b over number field \(\Q(\sqrt{-14}) \)

• Base field: \(\Q(\sqrt{-14}) \)
• Label: 2.0.56.1-30.2-b
• Conductor: 30.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-14}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 14 \); class number \(4\).

Elliptic curves in class 30.2-b over \(\Q(\sqrt{-14}) \)

Isogeny class 30.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30.2-b1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 378 a + 1167\) , \( 1895 a - 29621\bigr] \)
30.2-b2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -12 a - 213\) , \( 295 a - 2193\bigr] \)
30.2-b3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 23 a + 77\) , \( 15 a - 463\bigr] \)
30.2-b4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 3 a + 27\) , \( -15 a + 29\bigr] \)

Rank

Rank: \( 0 \)

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