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Properties

Label 141960.f
Number of curves $6$
Conductor $141960$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("f1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 141960.f have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 141960.f do not have complex multiplication.

Modular form 141960.2.a.f

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 4 q^{11} + q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 141960.f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141960.f1 141960cn3 \([0, -1, 0, -34449016, 77835447676]\) \(914732517663095044/9555\) \(47227043834880\) \([2]\) \(5505024\) \(2.6517\)  
141960.f2 141960cn6 \([0, -1, 0, -12965736, -17127975060]\) \(24385137179326562/1284775885575\) \(12700401269711626598400\) \([2]\) \(11010048\) \(2.9983\)  
141960.f3 141960cn4 \([0, -1, 0, -2318736, 1018771740]\) \(278944461825124/70849130625\) \(350182626655155840000\) \([2, 2]\) \(5505024\) \(2.6517\)  
141960.f4 141960cn2 \([0, -1, 0, -2153116, 1216654516]\) \(893359210685776/91298025\) \(112813600960569600\) \([2, 2]\) \(2752512\) \(2.3052\)  
141960.f5 141960cn1 \([0, -1, 0, -124271, 22070580]\) \(-2748251600896/1124136195\) \(-86815851252028080\) \([2]\) \(1376256\) \(1.9586\) \(\Gamma_0(N)\)-optimal
141960.f6 141960cn5 \([0, -1, 0, 5678344, 6498370956]\) \(2048324060764798/3031899609375\) \(-29971251858693600000000\) \([2]\) \(11010048\) \(2.9983\)