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Properties

Label 372645.br
Number of curves $4$
Conductor $372645$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("br1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 372645.br have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 372645.br do not have complex multiplication.

Modular form 372645.2.a.br

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{8} - q^{10} - 4 q^{11} - q^{16} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 372645.br

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372645.br1 372645br3 \([1, -1, 1, -1800696722, 29387256716094]\) \(1559802282754777489/1481059636875\) \(613124158372614236894056875\) \([2]\) \(222953472\) \(4.0619\)  
372645.br2 372645br2 \([1, -1, 1, -139072667, 226419200466]\) \(718576775407009/362361861225\) \(150009361985376509317454025\) \([2, 2]\) \(111476736\) \(3.7154\)  
372645.br3 372645br1 \([1, -1, 1, -76095662, -252986952396]\) \(117713838907729/1322517105\) \(547491246637050644091345\) \([2]\) \(55738368\) \(3.3688\) \(\Gamma_0(N)\)-optimal
372645.br4 372645br4 \([1, -1, 1, 514919308, 1746819743946]\) \(36472485598112591/24291459037755\) \(-10056097679896046122329999195\) \([2]\) \(222953472\) \(4.0619\)