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Properties

Label 143650.bi
Number of curves $2$
Conductor $143650$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bi1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 143650.bi have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(5\)\(1\)
\(13\)\(1\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(7\) \( 1 + 3 T + 7 T^{2}\) 1.7.d
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 + 3 T + 23 T^{2}\) 1.23.d
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 143650.bi do not have complex multiplication.

Modular form 143650.2.a.bi

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3 q^{7} + q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{14} + q^{16} + q^{17} - 3 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 143650.bi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143650.bi1 143650i2 \([1, -1, 1, -21575755, -38226393253]\) \(420644261295449288721/4302712843796480\) \(11361851103150080000000\) \([]\) \(9483264\) \(3.0496\)  
143650.bi2 143650i1 \([1, -1, 1, -1929505, 1032095497]\) \(300853103177579121/10625000\) \(28056640625000\) \([]\) \(1354752\) \(2.0766\) \(\Gamma_0(N)\)-optimal