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Properties

Label 798.d
Number of curves $6$
Conductor $798$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 798.d have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(7\)\(1 - T\)
\(19\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 798.d do not have complex multiplication.

Modular form 798.2.a.d

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + 6 q^{11} + q^{12} - 4 q^{13} - q^{14} + q^{16} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 798.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
798.d1 798e6 \([1, 0, 1, -9786711, -11785100294]\) \(103665426767620308239307625/5961940992\) \(5961940992\) \([2]\) \(20736\) \(2.2622\)  
798.d2 798e5 \([1, 0, 1, -611671, -184179718]\) \(25309080274342544331625/191933498523648\) \(191933498523648\) \([2]\) \(10368\) \(1.9157\)  
798.d3 798e4 \([1, 0, 1, -120936, -16143626]\) \(195607431345044517625/752875610010048\) \(752875610010048\) \([6]\) \(6912\) \(1.7129\)  
798.d4 798e3 \([1, 0, 1, -11176, 13046]\) \(154357248921765625/89242711068672\) \(89242711068672\) \([6]\) \(3456\) \(1.3664\)  
798.d5 798e2 \([1, 0, 1, -7941, 254500]\) \(55369510069623625/3916046302812\) \(3916046302812\) \([6]\) \(2304\) \(1.1636\)  
798.d6 798e1 \([1, 0, 1, -7801, 264524]\) \(52492168638015625/293197968\) \(293197968\) \([6]\) \(1152\) \(0.81705\) \(\Gamma_0(N)\)-optimal