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Properties

Label 11830.d
Number of curves $6$
Conductor $11830$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 11830.d have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 2 T + 3 T^{2}\) 1.3.c
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 11830.d do not have complex multiplication.

Modular form 11830.2.a.d

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + q^{5} + 2 q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 2 q^{12} + q^{14} - 2 q^{15} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 6 & 18 \\ 2 & 1 & 6 & 18 & 3 & 9 \\ 3 & 6 & 1 & 3 & 2 & 6 \\ 9 & 18 & 3 & 1 & 6 & 2 \\ 6 & 3 & 2 & 6 & 1 & 3 \\ 18 & 9 & 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 11830.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.d1 11830i6 \([1, 0, 1, -89408778, -325253059402]\) \(16375858190544687071329/9025573730468750\) \(43564720512390136718750\) \([2]\) \(1741824\) \(3.2920\)  
11830.d2 11830i5 \([1, 0, 1, -89396948, -325343468994]\) \(16369358802802724130049/4976562500\) \(24020916664062500\) \([2]\) \(870912\) \(2.9454\)  
11830.d3 11830i4 \([1, 0, 1, -3440168, 1928275806]\) \(932829715460155969/206949435875000\) \(998905399626372875000\) \([2]\) \(580608\) \(2.7427\)  
11830.d4 11830i2 \([1, 0, 1, -3230608, 2234714718]\) \(772531501373731009/15142400\) \(73089472601600\) \([2]\) \(193536\) \(2.1934\)  
11830.d5 11830i3 \([1, 0, 1, -1121488, -431212962]\) \(32318182904349889/2067798824000\) \(9980869973872616000\) \([2]\) \(290304\) \(2.3961\)  
11830.d6 11830i1 \([1, 0, 1, -202128, 34826846]\) \(189208196468929/834928640\) \(4030041073909760\) \([2]\) \(96768\) \(1.8468\) \(\Gamma_0(N)\)-optimal