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Properties

Label 29400r
Number of curves $6$
Conductor $29400$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 29400r have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 2 T + 11 T^{2}\) 1.11.c
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
\(29\) \( 1 + 8 T + 29 T^{2}\) 1.29.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29400r do not have complex multiplication.

Modular form 29400.2.a.r

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 29400r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.i4 29400r1 \([0, -1, 0, -214783, -38241188]\) \(37256083456/525\) \(15441431250000\) \([2]\) \(147456\) \(1.6709\) \(\Gamma_0(N)\)-optimal
29400.i3 29400r2 \([0, -1, 0, -220908, -35938188]\) \(2533446736/275625\) \(129708022500000000\) \([2, 2]\) \(294912\) \(2.0174\)  
29400.i5 29400r3 \([0, -1, 0, 293592, -178969188]\) \(1486779836/8203125\) \(-15441431250000000000\) \([2]\) \(589824\) \(2.3640\)  
29400.i2 29400r4 \([0, -1, 0, -833408, 254386812]\) \(34008619684/4862025\) \(9152198067600000000\) \([2, 2]\) \(589824\) \(2.3640\)  
29400.i6 29400r5 \([0, -1, 0, 1371592, 1370116812]\) \(75798394558/259416045\) \(-976641224902560000000\) \([2]\) \(1179648\) \(2.7106\)  
29400.i1 29400r6 \([0, -1, 0, -12838408, 17709656812]\) \(62161150998242/1607445\) \(6051657497760000000\) \([2]\) \(1179648\) \(2.7106\)