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Properties

Label 80850.bv
Number of curves $4$
Conductor $80850$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 80850.bv have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 6 T + 13 T^{2}\) 1.13.g
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 80850.bv do not have complex multiplication.

Modular form 80850.2.a.bv

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - q^{11} + q^{12} - 6 q^{13} + q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 80850.bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.bv1 80850ch4 \([1, 0, 1, -118618001, -497258281852]\) \(100407751863770656369/166028940000\) \(305205293157187500000\) \([2]\) \(11796480\) \(3.1934\)  
80850.bv2 80850ch2 \([1, 0, 1, -7486001, -7610689852]\) \(25238585142450289/995844326400\) \(1830626393072400000000\) \([2, 2]\) \(5898240\) \(2.8468\)  
80850.bv3 80850ch1 \([1, 0, 1, -1214001, 354750148]\) \(107639597521009/32699842560\) \(60110996520960000000\) \([2]\) \(2949120\) \(2.5002\) \(\Gamma_0(N)\)-optimal
80850.bv4 80850ch3 \([1, 0, 1, 3293999, -27726169852]\) \(2150235484224911/181905111732960\) \(-334389913910484547500000\) \([2]\) \(11796480\) \(3.1934\)