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Properties

Label 910.g
Number of curves $6$
Conductor $910$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("g1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 910.g have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 2 T + 3 T^{2}\) 1.3.c
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 - 6 T + 23 T^{2}\) 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 910.g do not have complex multiplication.

Modular form 910.2.a.g

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{12} + q^{13} + q^{14} + 2 q^{15} + q^{16} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 910.g

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
910.g1 910j6 \([1, 0, 0, -529046, -148084874]\) \(16375858190544687071329/9025573730468750\) \(9025573730468750\) \([2]\) \(10368\) \(2.0095\)  
910.g2 910j5 \([1, 0, 0, -528976, -148126020]\) \(16369358802802724130049/4976562500\) \(4976562500\) \([2]\) \(5184\) \(1.6630\)  
910.g3 910j4 \([1, 0, 0, -20356, 876120]\) \(932829715460155969/206949435875000\) \(206949435875000\) \([6]\) \(3456\) \(1.4602\)  
910.g4 910j2 \([1, 0, 0, -19116, 1015696]\) \(772531501373731009/15142400\) \(15142400\) \([6]\) \(1152\) \(0.91093\)  
910.g5 910j3 \([1, 0, 0, -6636, -196784]\) \(32318182904349889/2067798824000\) \(2067798824000\) \([6]\) \(1728\) \(1.1137\)  
910.g6 910j1 \([1, 0, 0, -1196, 15760]\) \(189208196468929/834928640\) \(834928640\) \([6]\) \(576\) \(0.56436\) \(\Gamma_0(N)\)-optimal