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Properties

Label 19110.cu
Number of curves $8$
Conductor $19110$
CM no
Rank $0$
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Show commands: SageMath
Copy content sage:E = EllipticCurve("cu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 19110.cu have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 19110.cu do not have complex multiplication.

Modular form 19110.2.a.cu

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} - q^{13} - q^{15} + q^{16} - 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 19110.cu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.cu1 19110cm7 \([1, 0, 0, -451682981, 3692738629341]\) \(86623684689189325642735681/56690726941459561860\) \(6669607333935775993267140\) \([2]\) \(6291456\) \(3.7030\)  
19110.cu2 19110cm3 \([1, 0, 0, -273960961, -1745367222775]\) \(19328649688935739391016961/1048320\) \(123333799680\) \([2]\) \(1572864\) \(3.0098\)  
19110.cu3 19110cm5 \([1, 0, 0, -33747281, 33544401561]\) \(36128658497509929012481/16775330746084419600\) \(1973600886946085881520400\) \([2, 2]\) \(3145728\) \(3.3564\)  
19110.cu4 19110cm4 \([1, 0, 0, -17185281, -27062581239]\) \(4770955732122964500481/71987251059360000\) \(8469228099882644640000\) \([2, 2]\) \(1572864\) \(3.0098\)  
19110.cu5 19110cm2 \([1, 0, 0, -17122561, -27272429815]\) \(4718909406724749250561/1098974822400\) \(129293288880537600\) \([2, 2]\) \(786432\) \(2.6632\)  
19110.cu6 19110cm6 \([1, 0, 0, -1626801, -74239004295]\) \(-4047051964543660801/20235220197806250000\) \(-2380653421051707506250000\) \([2]\) \(3145728\) \(3.3564\)  
19110.cu7 19110cm1 \([1, 0, 0, -1066241, -429474039]\) \(-1139466686381936641/17587891077120\) \(-2069197797332090880\) \([2]\) \(393216\) \(2.3167\) \(\Gamma_0(N)\)-optimal
19110.cu8 19110cm8 \([1, 0, 0, 119196419, 253263320981]\) \(1591934139020114746758719/1156766383092650262660\) \(-136092408204467210751686340\) \([2]\) \(6291456\) \(3.7030\)