Properties

 Label 2.107.abh_sc Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $1 - 33 x + 470 x^{2} - 3531 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0392440067605$, $\pm0.294089326573$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3}, \sqrt{65})$$ Galois group: $C_2^2$ Jacobians: 20

This isogeny class is simple but not geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 20 curves, and hence is principally polarizable:

• $y^2=82x^6+16x^5+63x^4+45x^3+34x^2+100x+2$
• $y^2=80x^6+103x^5+29x^4+35x^3+21x^2+15x+94$
• $y^2=78x^6+83x^5+93x^4+65x^3+49x^2+41x+78$
• $y^2=31x^6+84x^5+43x^4+87x^3+26x^2+106x+77$
• $y^2=18x^6+95x^5+2x^4+48x^3+95x^2+74x+16$
• $y^2=102x^6+76x^5+38x^4+12x^3+25x^2+53x+45$
• $y^2=17x^6+18x^5+43x^4+94x^3+69x^2+40x+66$
• $y^2=22x^6+84x^5+44x^4+18x^3+89x^2+57x+93$
• $y^2=104x^6+30x^5+62x^4+93x^3+12x^2+90x+100$
• $y^2=12x^6+90x^5+85x^4+54x^3+29x^2+89x+12$
• $y^2=96x^6+103x^5+10x^4+71x^3+24x^2+18x+95$
• $y^2=34x^6+5x^5+72x^4+28x^3+88x^2+97x+85$
• $y^2=78x^6+65x^5+99x^4+54x^3+45x^2+21x+98$
• $y^2=35x^6+85x^5+10x^4+91x^3+37x^2+46x+77$
• $y^2=81x^6+80x^5+28x^4+38x^3+94x^2+85x+81$
• $y^2=106x^6+18x^4+54x^3+47x^2+73x+19$
• $y^2=106x^6+59x^5+51x^3+56x^2+79x+78$
• $y^2=72x^6+37x^5+32x^4+3x^3+61x^2+70x+97$
• $y^2=67x^6+73x^5+74x^4+83x^3+60x^2+64x+47$
• $y^2=94x^6+59x^5+50x^4+93x^3+30x^2+25x+53$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8356 129384304 1500728542096 17181770305242816 196712733139572209836 2252186157061585644073216 25785334855288484118008241916 295216370360504704207504206699264 3379932275732534794112001482505825424 38696844628455670531691341403541463984624

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 11301 1225044 131078905 14025346005 1500726732342 160578106255383 17181861536645809 1838459212420154508 196715135747225994261

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3}, \sqrt{65})$$.
Endomorphism algebra over $\overline{\F}_{107}$
 The base change of $A$ to $\F_{107^{6}}$ is 1.1500730351849.adyzdy 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-195})$$$)$
All geometric endomorphisms are defined over $\F_{107^{6}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{107^{2}}$  The base change of $A$ to $\F_{107^{2}}$ is the simple isogeny class 2.11449.aft_pxo and its endomorphism algebra is $$\Q(\sqrt{-3}, \sqrt{65})$$.
• Endomorphism algebra over $\F_{107^{3}}$  The base change of $A$ to $\F_{107^{3}}$ is the simple isogeny class 2.1225043.a_adyzdy and its endomorphism algebra is $$\Q(\sqrt{-3}, \sqrt{65})$$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.bh_sc $2$ (not in LMFDB) 2.107.a_ft $3$ (not in LMFDB) 2.107.bh_sc $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.bh_sc $2$ (not in LMFDB) 2.107.a_ft $3$ (not in LMFDB) 2.107.bh_sc $3$ (not in LMFDB) 2.107.a_ft $6$ (not in LMFDB) 2.107.a_aft $12$ (not in LMFDB)