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Properties

Label 19110.dd
Number of curves $1$
Conductor $19110$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 19110.dd1 has 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 \(\mathbb{F}_p\)
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 - T + 23 T^{2}\) 1.23.ab
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 19110.2.a.dd

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

Elliptic curves in class 19110.dd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.dd1 19110cx1 \([1, 0, 0, -872985, 617314725]\) \(-12763205672220241/21177624487500\) \(-122084790823164487500\) \([]\) \(776160\) \(2.5451\) \(\Gamma_0(N)\)-optimal