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Properties

Label 152880db
Number of curves $4$
Conductor $152880$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("db1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 152880db have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 3 T + 11 T^{2}\) 1.11.d
\(17\) \( 1 - 5 T + 17 T^{2}\) 1.17.af
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 - 5 T + 23 T^{2}\) 1.23.af
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 152880db do not have complex multiplication.

Modular form 152880.2.a.db

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4 q^{11} - q^{13} - q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 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 152880db

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.cq4 152880db1 \([0, -1, 0, -564514120, 2615444412400]\) \(41285728533151645510969/17760741842188800000\) \(8558729285597880857395200000\) \([2]\) \(132710400\) \(4.0561\) \(\Gamma_0(N)\)-optimal
152880.cq2 152880db2 \([0, -1, 0, -7729897800, 261474961389552]\) \(105997782562506306791694649/51649016225625000000\) \(24889160130267363840000000000\) \([2, 2]\) \(265420800\) \(4.4027\)  
152880.cq1 152880db3 \([0, -1, 0, -123663897800, 16738386030189552]\) \(434014578033107719741685694649/103121648659575000\) \(49693322621543789260800000\) \([2]\) \(530841600\) \(4.7492\)  
152880.cq3 152880db4 \([0, -1, 0, -6442036680, 351458332988400]\) \(-61354313914516350666047929/75227254486083984375000\) \(-36251284533384375000000000000000\) \([2]\) \(530841600\) \(4.7492\)