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Properties

Label 33600.i
Number of curves $8$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 33600.i have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 33600.i do not have complex multiplication.

Modular form 33600.2.a.i

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 33600.i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.i1 33600eq8 \([0, -1, 0, -3073280033, 65577989759937]\) \(783736670177727068275201/360150\) \(1475174400000000\) \([2]\) \(9437184\) \(3.6389\)  
33600.i2 33600eq6 \([0, -1, 0, -192080033, 1024703759937]\) \(191342053882402567201/129708022500\) \(531284060160000000000\) \([2, 2]\) \(4718592\) \(3.2923\)  
33600.i3 33600eq7 \([0, -1, 0, -190880033, 1038137759937]\) \(-187778242790732059201/4984939585440150\) \(-20418312541962854400000000\) \([2]\) \(9437184\) \(3.6389\)  
33600.i4 33600eq4 \([0, -1, 0, -24112033, -45551504063]\) \(378499465220294881/120530818800\) \(493694233804800000000\) \([2]\) \(2359296\) \(2.9457\)  
33600.i5 33600eq3 \([0, -1, 0, -12080033, 15803759937]\) \(47595748626367201/1215506250000\) \(4978713600000000000000\) \([2, 2]\) \(2359296\) \(2.9457\)  
33600.i6 33600eq2 \([0, -1, 0, -1712033, -505104063]\) \(135487869158881/51438240000\) \(210691031040000000000\) \([2, 2]\) \(1179648\) \(2.5991\)  
33600.i7 33600eq1 \([0, -1, 0, 335967, -56592063]\) \(1023887723039/928972800\) \(-3805072588800000000\) \([2]\) \(589824\) \(2.2526\) \(\Gamma_0(N)\)-optimal
33600.i8 33600eq5 \([0, -1, 0, 2031967, 50505167937]\) \(226523624554079/269165039062500\) \(-1102500000000000000000000\) \([2]\) \(4718592\) \(3.2923\)