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Properties

Label 28.96.2-14.a.1.3
Level $28$
Index $96$
Genus $2$
Analytic rank $0$
Cusps $6$
$\Q$-cusps $6$

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Invariants

Level: $28$ $\SL_2$-level: $28$ Newform level: $14$
Index: $96$ $\PSL_2$-index:$48$
Genus: $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (all of which are rational) Cusp widths $2^{3}\cdot14^{3}$ Cusp orbits $1^{6}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $0$
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $6$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 14E2
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 28.96.2.67

Level structure

$\GL_2(\Z/28\Z)$-generators: $\begin{bmatrix}3&0\\14&17\end{bmatrix}$, $\begin{bmatrix}3&8\\20&11\end{bmatrix}$, $\begin{bmatrix}5&16\\4&19\end{bmatrix}$, $\begin{bmatrix}5&22\\18&23\end{bmatrix}$, $\begin{bmatrix}21&4\\2&23\end{bmatrix}$
Contains $-I$: no $\quad$ (see 14.48.2.a.1 for the level structure with $-I$)
Cyclic 28-isogeny field degree: $2$
Cyclic 28-torsion field degree: $24$
Full 28-torsion field degree: $2016$

Jacobian

Conductor: $2^{2}\cdot7^{2}$
Simple: no
Squarefree: no
Decomposition: $1^{2}$
Newforms: 14.2.a.a$^{2}$

Models

Embedded model Embedded model in $\mathbb{P}^{3}$

$ 0 $ $=$ $ x y^{2} + 2 x y z + x y w + y^{3} - y^{2} z + y^{2} w - y z^{2} + y z w + 2 z^{3} + z^{2} w $
$=$ $x y^{2} - x y w - y^{3} - 2 y^{2} w + 4 y z^{2} - y w^{2}$
$=$ $x^{2} y - x y z + x y w + x z^{2} + y^{3} - 2 y^{2} z + 2 y^{2} w - 2 y z w + y w^{2}$
$=$ $x y^{2} + x y z + x y w + x z w + y^{3} + y^{2} w - y z^{2} + 3 y z w - 2 z^{3} + z^{2} w + z w^{2}$
$=$$\cdots$
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Singular plane model Singular plane model

$ 0 $ $=$ $ 2 x^{4} + x^{3} y + 3 x^{3} z - 5 x^{2} y^{2} + 6 x^{2} y z + 2 x^{2} z^{2} - 6 x y^{3} + \cdots - y^{2} z^{2} $
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Weierstrass model Weierstrass model

$ y^{2} + \left(x^{2} + x\right) y $ $=$ $ x^{6} - 3x^{5} + 6x^{4} - 8x^{3} + 6x^{2} - 3x + 1 $
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Rational points

This modular curve has 6 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.

Embedded model
$(0:-1:0:1)$, $(1/2:-1/2:1/2:1)$, $(1:0:0:0)$, $(-1:0:0:1)$, $(-1:1:1:1)$, $(0:0:-1/2:1)$

Maps to other modular curves

$j$-invariant map of degree 48 from the embedded model of this modular curve to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle -3\,\frac{5008426795008x^{10}-22634236477440x^{9}z+24367922675712x^{9}w-53359008546816x^{8}zw+38911623561216x^{8}w^{2}-58560067141632x^{7}zw^{2}+32790213033984x^{7}w^{3}-40837941559296x^{6}zw^{3}+22706770673664x^{6}w^{4}-2358274507416576x^{5}zw^{4}-1209548649738240x^{5}w^{5}+22306833811196928x^{4}zw^{5}+18192961603553280x^{4}w^{6}+38398604279166752x^{3}zw^{6}-15623411137975712x^{3}w^{7}+2432355423805892x^{2}zw^{7}-32829140341326517x^{2}w^{8}+189599554173625344xz^{9}+66176393521932288xz^{8}w-1028333486184238080xz^{7}w^{2}-545127327389260800xz^{6}w^{3}+365145024994737120xz^{5}w^{4}+626910665797517984xz^{4}w^{5}-84785638599898540xz^{3}w^{6}-218042342780958445xz^{2}w^{7}+109419570029704523xzw^{8}-37143481555477727xw^{9}-33791680096059919y^{2}w^{8}+126721196224939008yz^{9}-441050065082855424yz^{8}w-886093154669786112yz^{7}w^{2}+322409985823448064yz^{6}w^{3}+680811059998208736yz^{5}w^{4}+304996813852998240yz^{4}w^{5}-482141075002789228yz^{3}w^{6}+46282289454473575yz^{2}w^{7}+108594543334801201yzw^{8}-73103511080186329yw^{9}-155686164491999232z^{10}+1051106553239049216z^{9}w+683703187255388160z^{8}w^{2}-1750614116203330560z^{7}w^{3}-1364596939347119424z^{6}w^{4}+648708673990469920z^{5}w^{5}+1163885470942954856z^{4}w^{6}-530900017712072486z^{3}w^{7}-47709446343759039z^{2}w^{8}+120745945332226727zw^{9}-39353439452884938w^{10}}{4081839381504x^{5}zw^{4}+4886575423488x^{5}w^{5}-30645958652928x^{4}zw^{5}-21512576808960x^{4}w^{6}-50964446096096x^{3}zw^{6}+5768109449696x^{3}w^{7}-7204163652092x^{2}zw^{7}+7122489037099x^{2}w^{8}-330628989901824xz^{9}-333960830724096xz^{8}w+1578651649348608xz^{7}w^{2}+1000299314414592xz^{6}w^{3}-621452206617120xz^{5}w^{4}-608605481337056xz^{4}w^{5}+183983104586644xz^{3}w^{6}+306223780092979xz^{2}w^{7}-93435884675861xzw^{8}-33349371489343xw^{9}-29995420060463y^{2}w^{8}-216503839374336yz^{9}+602545605083136yz^{8}w+1611440487336960yz^{7}w^{2}-190331052106752yz^{6}w^{3}-1050521700985632yz^{5}w^{4}-40870585110816yz^{4}w^{5}+576464923458772yz^{3}w^{6}+26175502310855yz^{2}w^{7}-59086726653103yzw^{8}-38300018904761yw^{9}+255283317467136z^{10}-1557013511752704z^{9}w-1846619142432768z^{8}w^{2}+2770407011386368z^{7}w^{3}+1925247215888064z^{6}w^{4}-1229556901877728z^{5}w^{5}-1209462663370136z^{4}w^{6}+610877203701722z^{3}w^{7}+264330635858913z^{2}w^{8}-102468369085433zw^{9}-8304598844298w^{10}}$

Map of degree 1 from the embedded model of this modular curve to the plane model of the modular curve 14.48.2.a.1 :

$\displaystyle X$ $=$ $\displaystyle y$
$\displaystyle Y$ $=$ $\displaystyle z$
$\displaystyle Z$ $=$ $\displaystyle w$

Equation of the image curve:

$0$ $=$ $ 2X^{4}+X^{3}Y-5X^{2}Y^{2}-6XY^{3}+3X^{3}Z+6X^{2}YZ-2XY^{2}Z-2Y^{3}Z+2X^{2}Z^{2}+XYZ^{2}-Y^{2}Z^{2}+XZ^{3} $

Map of degree 1 from the embedded model of this modular curve to the Weierstrass model of the modular curve 14.48.2.a.1 :

$\displaystyle X$ $=$ $\displaystyle \frac{1}{2}y^{2}-\frac{1}{3}yw-\frac{1}{6}w^{2}$
$\displaystyle Y$ $=$ $\displaystyle -\frac{31}{24}y^{6}-\frac{17}{6}y^{5}z-\frac{23}{18}y^{5}w-\frac{11}{6}y^{4}z^{2}-\frac{61}{18}y^{4}zw-\frac{235}{216}y^{4}w^{2}-\frac{17}{9}y^{3}z^{2}w-\frac{58}{27}y^{3}zw^{2}-\frac{20}{27}y^{3}w^{3}-\frac{22}{27}y^{2}z^{2}w^{2}-\frac{8}{9}y^{2}zw^{3}-\frac{61}{216}y^{2}w^{4}-\frac{5}{27}yz^{2}w^{3}-\frac{11}{54}yzw^{4}-\frac{1}{18}yw^{5}-\frac{1}{54}z^{2}w^{4}-\frac{1}{54}zw^{5}-\frac{1}{216}w^{6}$
$\displaystyle Z$ $=$ $\displaystyle y^{2}+yz+\frac{1}{3}yw+\frac{1}{3}zw$

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
28.12.0-2.a.1.1 $28$ $8$ $8$ $0$ $0$ full Jacobian

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
28.192.4-28.a.1.1 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.1.4 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.1.5 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.1.8 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.1.10 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.1.11 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.1 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.4 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.5 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.8 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.10 $28$ $2$ $2$ $4$ $0$ $2$
28.192.4-28.a.2.11 $28$ $2$ $2$ $4$ $0$ $2$
28.192.5-28.a.1.1 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.a.1.9 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.b.1.1 $28$ $2$ $2$ $5$ $0$ $1^{3}$
28.192.5-28.b.1.7 $28$ $2$ $2$ $5$ $0$ $1^{3}$
28.192.5-28.b.1.12 $28$ $2$ $2$ $5$ $0$ $1^{3}$
28.192.5-28.c.1.1 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.c.1.3 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.c.1.8 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.d.1.1 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.d.1.4 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.5-28.d.1.10 $28$ $2$ $2$ $5$ $1$ $1^{3}$
28.192.6-28.a.1.2 $28$ $2$ $2$ $6$ $0$ $2^{2}$
28.192.6-28.a.1.4 $28$ $2$ $2$ $6$ $0$ $2^{2}$
28.192.6-28.a.2.2 $28$ $2$ $2$ $6$ $0$ $2^{2}$
28.192.6-28.a.2.4 $28$ $2$ $2$ $6$ $0$ $2^{2}$
28.288.4-14.a.1.4 $28$ $3$ $3$ $4$ $0$ $2$
28.288.4-14.a.2.4 $28$ $3$ $3$ $4$ $0$ $2$
28.288.4-14.b.1.3 $28$ $3$ $3$ $4$ $0$ $1^{2}$
28.672.17-14.a.1.4 $28$ $7$ $7$ $17$ $1$ $1^{9}\cdot2^{3}$
56.192.4-56.a.1.6 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.1.8 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.1.13 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.1.15 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.1.17 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.1.19 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.6 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.8 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.13 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.15 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.17 $56$ $2$ $2$ $4$ $0$ $2$
56.192.4-56.a.2.19 $56$ $2$ $2$ $4$ $0$ $2$
56.192.5-56.a.1.7 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.a.1.9 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.a.1.14 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.b.1.7 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.b.1.9 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.b.1.14 $56$ $2$ $2$ $5$ $1$ $1^{3}$
56.192.5-56.c.1.1 $56$ $2$ $2$ $5$ $0$ $1^{3}$
56.192.5-56.c.1.3 $56$ $2$ $2$ $5$ $0$ $1^{3}$
56.192.5-56.c.1.19 $56$ $2$ $2$ $5$ $0$ $1^{3}$
56.192.5-56.d.1.1 $56$ $2$ $2$ $5$ $3$ $1^{3}$
56.192.5-56.d.1.5 $56$ $2$ $2$ $5$ $3$ $1^{3}$
56.192.5-56.d.1.19 $56$ $2$ $2$ $5$ $3$ $1^{3}$
56.192.6-56.a.1.5 $56$ $2$ $2$ $6$ $2$ $2^{2}$
56.192.6-56.a.1.6 $56$ $2$ $2$ $6$ $2$ $2^{2}$
56.192.6-56.a.2.5 $56$ $2$ $2$ $6$ $2$ $2^{2}$
56.192.6-56.a.2.6 $56$ $2$ $2$ $6$ $2$ $2^{2}$
84.192.4-84.a.1.2 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.1.8 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.1.9 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.1.15 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.1.17 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.1.23 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.2 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.8 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.9 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.15 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.17 $84$ $2$ $2$ $4$ $?$ not computed
84.192.4-84.a.2.23 $84$ $2$ $2$ $4$ $?$ not computed
84.192.5-84.a.1.1 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.a.1.11 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.a.1.18 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.b.1.1 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.b.1.2 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.b.1.13 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.c.1.3 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.c.1.8 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.c.1.14 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.d.1.2 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.d.1.5 $84$ $2$ $2$ $5$ $?$ not computed
84.192.5-84.d.1.17 $84$ $2$ $2$ $5$ $?$ not computed
84.192.6-84.a.1.3 $84$ $2$ $2$ $6$ $?$ not computed
84.192.6-84.a.1.5 $84$ $2$ $2$ $6$ $?$ not computed
84.192.6-84.a.2.5 $84$ $2$ $2$ $6$ $?$ not computed
84.192.6-84.a.2.7 $84$ $2$ $2$ $6$ $?$ not computed
84.288.10-42.a.1.3 $84$ $3$ $3$ $10$ $?$ not computed
84.384.11-42.a.1.11 $84$ $4$ $4$ $11$ $?$ not computed
140.192.4-140.a.1.2 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.1.7 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.1.10 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.1.15 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.1.18 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.1.23 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.2 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.7 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.10 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.15 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.18 $140$ $2$ $2$ $4$ $?$ not computed
140.192.4-140.a.2.23 $140$ $2$ $2$ $4$ $?$ not computed
140.192.5-140.a.1.1 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.a.1.2 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.a.1.13 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.b.1.1 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.b.1.11 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.b.1.15 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.c.1.1 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.c.1.6 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.c.1.17 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.d.1.1 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.d.1.8 $140$ $2$ $2$ $5$ $?$ not computed
140.192.5-140.d.1.19 $140$ $2$ $2$ $5$ $?$ not computed
140.192.6-140.a.1.3 $140$ $2$ $2$ $6$ $?$ not computed
140.192.6-140.a.1.5 $140$ $2$ $2$ $6$ $?$ not computed
140.192.6-140.a.2.2 $140$ $2$ $2$ $6$ $?$ not computed
140.192.6-140.a.2.6 $140$ $2$ $2$ $6$ $?$ not computed
140.480.18-70.a.1.4 $140$ $5$ $5$ $18$ $?$ not computed
168.192.4-168.a.1.6 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.1.15 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.1.18 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.1.27 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.1.34 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.1.43 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.6 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.15 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.18 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.27 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.34 $168$ $2$ $2$ $4$ $?$ not computed
168.192.4-168.a.2.43 $168$ $2$ $2$ $4$ $?$ not computed
168.192.5-168.m.1.3 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.m.1.20 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.m.1.33 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.n.1.2 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.n.1.5 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.n.1.26 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.o.1.3 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.o.1.14 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.o.1.25 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.p.1.5 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.p.1.10 $168$ $2$ $2$ $5$ $?$ not computed
168.192.5-168.p.1.34 $168$ $2$ $2$ $5$ $?$ not computed
168.192.6-168.a.1.9 $168$ $2$ $2$ $6$ $?$ not computed
168.192.6-168.a.1.17 $168$ $2$ $2$ $6$ $?$ not computed
168.192.6-168.a.2.3 $168$ $2$ $2$ $6$ $?$ not computed
168.192.6-168.a.2.16 $168$ $2$ $2$ $6$ $?$ not computed
252.288.4-126.a.1.4 $252$ $3$ $3$ $4$ $?$ not computed
252.288.4-126.a.2.2 $252$ $3$ $3$ $4$ $?$ not computed
252.288.4-126.b.1.7 $252$ $3$ $3$ $4$ $?$ not computed
252.288.4-126.b.2.9 $252$ $3$ $3$ $4$ $?$ not computed
252.288.4-126.c.1.6 $252$ $3$ $3$ $4$ $?$ not computed
252.288.4-126.c.2.6 $252$ $3$ $3$ $4$ $?$ not computed
280.192.4-280.a.1.4 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.1.13 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.1.20 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.1.29 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.1.36 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.1.45 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.4 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.13 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.20 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.29 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.36 $280$ $2$ $2$ $4$ $?$ not computed
280.192.4-280.a.2.45 $280$ $2$ $2$ $4$ $?$ not computed
280.192.5-280.a.1.1 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.a.1.4 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.a.1.27 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.b.1.1 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.b.1.20 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.b.1.32 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.c.1.1 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.c.1.12 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.c.1.35 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.d.1.1 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.d.1.14 $280$ $2$ $2$ $5$ $?$ not computed
280.192.5-280.d.1.40 $280$ $2$ $2$ $5$ $?$ not computed
280.192.6-280.a.1.15 $280$ $2$ $2$ $6$ $?$ not computed
280.192.6-280.a.1.17 $280$ $2$ $2$ $6$ $?$ not computed
280.192.6-280.a.2.2 $280$ $2$ $2$ $6$ $?$ not computed
280.192.6-280.a.2.5 $280$ $2$ $2$ $6$ $?$ not computed
308.192.4-308.a.1.4 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.1.8 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.1.9 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.1.13 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.1.20 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.1.25 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.4 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.8 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.9 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.13 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.20 $308$ $2$ $2$ $4$ $?$ not computed
308.192.4-308.a.2.25 $308$ $2$ $2$ $4$ $?$ not computed
308.192.5-308.a.1.2 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.a.1.8 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.a.1.13 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.b.1.2 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.b.1.8 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.b.1.18 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.c.1.5 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.c.1.8 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.c.1.13 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.d.1.6 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.d.1.8 $308$ $2$ $2$ $5$ $?$ not computed
308.192.5-308.d.1.18 $308$ $2$ $2$ $5$ $?$ not computed
308.192.6-308.a.1.4 $308$ $2$ $2$ $6$ $?$ not computed
308.192.6-308.a.1.10 $308$ $2$ $2$ $6$ $?$ not computed
308.192.6-308.a.2.4 $308$ $2$ $2$ $6$ $?$ not computed
308.192.6-308.a.2.10 $308$ $2$ $2$ $6$ $?$ not computed