Properties

Label 35280.bp
Number of curves $8$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.bp1 35280dx7 \([0, 0, 0, -37633323, 88860133978]\) \(16778985534208729/81000\) \(28455140560896000\) \([2]\) \(1327104\) \(2.7796\)  
35280.bp2 35280dx8 \([0, 0, 0, -3200043, 299882842]\) \(10316097499609/5859375000\) \(2058386904000000000000\) \([2]\) \(1327104\) \(2.7796\)  
35280.bp3 35280dx6 \([0, 0, 0, -2353323, 1386901978]\) \(4102915888729/9000000\) \(3161682284544000000\) \([2, 2]\) \(663552\) \(2.4330\)  
35280.bp4 35280dx5 \([0, 0, 0, -2035803, -1118013302]\) \(2656166199049/33750\) \(11856308567040000\) \([2]\) \(442368\) \(2.2303\)  
35280.bp5 35280dx4 \([0, 0, 0, -483483, 111452362]\) \(35578826569/5314410\) \(1866941772200386560\) \([2]\) \(442368\) \(2.2303\)  
35280.bp6 35280dx2 \([0, 0, 0, -130683, -16472918]\) \(702595369/72900\) \(25609626504806400\) \([2, 2]\) \(221184\) \(1.8837\)  
35280.bp7 35280dx3 \([0, 0, 0, -95403, 37117402]\) \(-273359449/1536000\) \(-539593776562176000\) \([2]\) \(331776\) \(2.0864\)  
35280.bp8 35280dx1 \([0, 0, 0, 10437, -1260182]\) \(357911/2160\) \(-758803748290560\) \([2]\) \(110592\) \(1.5371\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35280.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 35280.bp do not have complex multiplication.

Modular form 35280.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.