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Properties

Label 40950ev
Number of curves $4$
Conductor $40950$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ev1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 40950ev have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 + 23 T^{2}\) 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 40950ev do not have complex multiplication.

Modular form 40950.2.a.ev

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 4 q^{11} + q^{13} + q^{14} + q^{16} - 6 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.

Elliptic curves in class 40950ev

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40950.eg4 40950ev1 \([1, -1, 1, 194920, -22532453]\) \(71903073502287/60782804992\) \(-692354138112000000\) \([2]\) \(737280\) \(2.1109\) \(\Gamma_0(N)\)-optimal
40950.eg3 40950ev2 \([1, -1, 1, -957080, -197636453]\) \(8511781274893233/3440817243136\) \(39193058910096000000\) \([2, 2]\) \(1474560\) \(2.4575\)  
40950.eg2 40950ev3 \([1, -1, 1, -7041080, 7054491547]\) \(3389174547561866673/74853681183008\) \(852630212225200500000\) \([2]\) \(2949120\) \(2.8040\)  
40950.eg1 40950ev4 \([1, -1, 1, -13305080, -18670244453]\) \(22868021811807457713/8953460393696\) \(101985509796943500000\) \([2]\) \(2949120\) \(2.8040\)