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Properties

Label 47190.bd
Number of curves $4$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 47190.bd have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(11\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(17\) \( 1 + 17 T^{2}\) 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.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 47190.bd do not have complex multiplication.

Modular form 47190.2.a.bd

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} - 4 q^{14} - q^{15} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 47190.bd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.bd1 47190ba4 \([1, 0, 1, -429467987534, 108328858237708832]\) \(4944928228995290413834018379264689/189679641808585500000\) \(336029055922059536965500000\) \([2]\) \(290304000\) \(5.0301\)  
47190.bd2 47190ba3 \([1, 0, 1, -26840487534, 1692803811708832]\) \(-1207087636168285491836819264689/236446260657750000000000\) \(-418878973977104247750000000000\) \([2]\) \(145152000\) \(4.6835\)  
47190.bd3 47190ba2 \([1, 0, 1, -5345002094, 146070237519776]\) \(9532597152396244075685450929/313550122650789880627200\) \(555473168833355971713803059200\) \([2]\) \(96768000\) \(4.4808\)  
47190.bd4 47190ba1 \([1, 0, 1, 106773906, 7869896630176]\) \(75991146714893572533071/15147028085515223040000\) \(-26833884222203434043965440000\) \([2]\) \(48384000\) \(4.1342\) \(\Gamma_0(N)\)-optimal