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Properties

Label 223080.l
Number of curves $6$
Conductor $223080$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 223080.l have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(11\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 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 223080.l do not have complex multiplication.

Modular form 223080.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + q^{11} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 223080.l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
223080.l1 223080dp3 \([0, -1, 0, -8923256, 10262639100]\) \(15897679904620804/2475\) \(12233064729600\) \([2]\) \(4718592\) \(2.3579\)  
223080.l2 223080dp6 \([0, -1, 0, -4732056, -3884567220]\) \(1185450336504002/26043266205\) \(257445625257348802560\) \([2]\) \(9437184\) \(2.7044\)  
223080.l3 223080dp4 \([0, -1, 0, -642256, 108713500]\) \(5927735656804/2401490025\) \(11869730474066150400\) \([2, 2]\) \(4718592\) \(2.3579\)  
223080.l4 223080dp2 \([0, -1, 0, -557756, 160461300]\) \(15529488955216/6125625\) \(7569208801440000\) \([2, 2]\) \(2359296\) \(2.0113\)  
223080.l5 223080dp1 \([0, -1, 0, -29631, 3291300]\) \(-37256083456/38671875\) \(-2986588068750000\) \([2]\) \(1179648\) \(1.6647\) \(\Gamma_0(N)\)-optimal
223080.l6 223080dp5 \([0, -1, 0, 2095544, 788783020]\) \(102949393183198/86815346805\) \(-858196167263222261760\) \([2]\) \(9437184\) \(2.7044\)