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Properties

Label 181056.w
Number of curves $6$
Conductor $181056$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("w1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 181056.w have rank \(2\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(23\)\(1 + T\)
\(41\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 6 T + 13 T^{2}\) 1.13.g
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 181056.w do not have complex multiplication.

Modular form 181056.2.a.w

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 181056.w

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
181056.w1 181056cq6 \([0, -1, 0, -41685377, -103549744767]\) \(30558708894178043523937/9478135170529992\) \(2484636266143414222848\) \([2]\) \(15335424\) \(3.0817\)  
181056.w2 181056cq3 \([0, -1, 0, -20608897, 36017438593]\) \(3692734274560500693217/2597955705792\) \(681038500539138048\) \([2]\) \(7667712\) \(2.7351\)  
181056.w3 181056cq4 \([0, -1, 0, -2955137, -1154736255]\) \(10887214909148618977/4099319456261184\) \(1074611999542131818496\) \([2, 2]\) \(7667712\) \(2.7351\)  
181056.w4 181056cq2 \([0, -1, 0, -1296257, 555569025]\) \(918877186561273057/23897549574144\) \(6264599235564404736\) \([2, 2]\) \(3833856\) \(2.3886\)  
181056.w5 181056cq1 \([0, -1, 0, 14463, 27873153]\) \(1276229915423/1281494089728\) \(-335935986657656832\) \([2]\) \(1916928\) \(2.0420\) \(\Gamma_0(N)\)-optimal
181056.w6 181056cq5 \([0, -1, 0, 9233023, -8245807743]\) \(332059183270966325663/304129832126760648\) \(-79725810713037543309312\) \([4]\) \(15335424\) \(3.0817\)