Properties

Base field Q(13)\Q(\sqrt{13})
Label 2.2.13.1-675.1-g
Conductor 675.1
Rank 1 1

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Base field Q(13)\Q(\sqrt{13})

Generator aa, with minimal polynomial x2x3 x^{2} - x - 3 ; class number 11.

Elliptic curves in class 675.1-g over Q(13)\Q(\sqrt{13})

Isogeny class 675.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
675.1-g1 [1 \bigl[1 , a1 a - 1 , 0 0 , 83a219 83 a - 219 , 684a+1625] -684 a + 1625\bigr]
675.1-g2 [a+1 \bigl[a + 1 , a1 a - 1 , 0 0 , 82a177 82 a - 177 , 282a639] 282 a - 639\bigr]
675.1-g3 [a \bigl[a , 0 0 , a a , 53a72 -53 a - 72 , 53a71] -53 a - 71\bigr]
675.1-g4 [1 \bigl[1 , a1 a - 1 , 0 0 , 2a24 -2 a - 24 , a+44] a + 44\bigr]

Rank

Rank: 1 1

Isogeny matrix

(1362312662132631)\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)

Isogeny graph