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Properties

Label 171600bf
Number of curves $4$
Conductor $171600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bf1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 171600bf have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(11\)\(1 + T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 171600bf do not have complex multiplication.

Modular form 171600.2.a.bf

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{7} + q^{9} + q^{11} - q^{13} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.

Elliptic curves in class 171600bf

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
171600.ek4 171600bf1 \([0, 1, 0, 143792, -15042412]\) \(5137417856375/4510142208\) \(-288649101312000000\) \([2]\) \(1990656\) \(2.0378\) \(\Gamma_0(N)\)-optimal
171600.ek3 171600bf2 \([0, 1, 0, -720208, -134274412]\) \(645532578015625/252306960048\) \(16147645443072000000\) \([2]\) \(3981312\) \(2.3844\)  
171600.ek2 171600bf3 \([0, 1, 0, -1494208, 938273588]\) \(-5764706497797625/2612665516032\) \(-167210593026048000000\) \([2]\) \(5971968\) \(2.5871\)  
171600.ek1 171600bf4 \([0, 1, 0, -26070208, 51220769588]\) \(30618029936661765625/3678951124992\) \(235452871999488000000\) \([2]\) \(11943936\) \(2.9337\)