why K.ideal(1/2,a) not in all 6 ideal classes of Q[-26] ?

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why K.ideal(1/2,a) not in all 6 ideal classes of Q[-26] ?

K.ideal(3,a+2) should be in C1,but still in C2......

K.<a> = NumberField(x^2 +26);K;html(table(K.class_group(),frame=true).transpose());show(K.class_number());C0=K.class_group()[0];C0;C1=K.class_group()[1];C1;C2=K.class_group()[2];C2;C3=K.class_group()[3];C3;C4=K.class_group()[4];C4;C5=K.class_group()[5];C5

C0=K.class_group()[0].list(); show(C0);C1=K.class_group()[1].list(); show(C1);C2=K.class_group()[2].list(); show(C2);C3=K.class_group()[3].list(); show(C3);C4=K.class_group()[4].list(); show(C4);C5=K.class_group()[5].list(); show(C5);

II = K.ideal(1/2,a);II in C0;II in C1;II in C2;II in C3;II in C4;II in C5

III = K.ideal(2);III in C0;III in C1;III in C2;III in C3;III in C4;III in C5

I = K.ideal(5/2,a);III in C0;III in C1;III in C2;III in C3;III in C4;III in C5

I = K.ideal(3,a+2);III in C0;III in C1;III in C2;III in C3;III in C4;III in C5

I = K.ideal(5,a+2);III in C0;III in C1;III in C2;III in C3;III in C4;III in C5

I = K.ideal(6,a^3+2,a^5,a^123);III in C0;III in C1;III in C2;III in C3;III in C4;III in C5