Properties

 Label 2.113.abk_vd Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $( 1 - 19 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$ Frobenius angles: $\pm0.148111132014$, $\pm0.205038125192$ Angle rank: $2$ (numerical) Jacobians: 6

This isogeny class is not 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 6 curves, and hence is principally polarizable:

• $y^2=43x^6+19x^5+107x^4+28x^3+107x^2+19x+43$
• $y^2=4x^6+53x^5+46x^4+28x^3+46x^2+53x+4$
• $y^2=12x^6+79x^5+46x^4+51x^3+46x^2+79x+12$
• $y^2=35x^6+76x^5+93x^4+9x^3+93x^2+76x+35$
• $y^2=33x^6+106x^5+49x^4+2x^3+49x^2+106x+33$
• $y^2=111x^6+69x^5+89x^4+67x^3+89x^2+69x+111$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9215 160552945 2082577615040 26589151546802425 339465155397052785575 4334533248392388142366720 55347534092758806454278261815 706732556228489513136981543453225 9024267961176194529218518960111267520 115230877635623386408858265089680371428225

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12572 1443330 163076244 18424808598 2081956626974 235260584712294 26584442062552036 3004041936655364130 339456738958019549132

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.at $\times$ 1.113.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.ac_adt $2$ (not in LMFDB) 2.113.c_adt $2$ (not in LMFDB) 2.113.bk_vd $2$ (not in LMFDB)