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Properties

Label 19110.e
Number of curves $4$
Conductor $19110$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("e1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 19110.e 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.e
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 8 T + 19 T^{2}\) 1.19.i
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 19110.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 19110.e

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.e1 19110p3 \([1, 1, 0, -16216549192, 494082084186496]\) \(4008766897254067912673785886329/1423480510711669921875000000\) \(167471058604717254638671875000000\) \([4]\) \(82575360\) \(4.8843\)  
19110.e2 19110p2 \([1, 1, 0, -6854789512, -212818772194496]\) \(302773487204995438715379645049/8911747415025000000000000\) \(1048458171630276225000000000000\) \([2, 2]\) \(41287680\) \(4.5377\)  
19110.e3 19110p1 \([1, 1, 0, -6805617032, -216099982943424]\) \(296304326013275547793071733369/268420373544960000000\) \(31579388527190999040000000\) \([2]\) \(20643840\) \(4.1911\) \(\Gamma_0(N)\)-optimal
19110.e4 19110p4 \([1, 1, 0, 1720210488, -709721157194496]\) \(4784981304203817469820354951/1852343836482910078035000000\) \(-217926400018377887770739715000000\) \([2]\) \(82575360\) \(4.8843\)