Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.bj1 35280dy8 \([0, 0, 0, -45518403, -74365731902]\) \(29689921233686449/10380965400750\) \(3646812711557275610112000\) \([2]\) \(5308416\) \(3.4144\)  
35280.bj2 35280dy5 \([0, 0, 0, -40649763, -99755096798]\) \(21145699168383889/2593080\) \(910943899822817280\) \([2]\) \(1769472\) \(2.8651\)  
35280.bj3 35280dy6 \([0, 0, 0, -19058403, 31172624098]\) \(2179252305146449/66177562500\) \(23248047443394816000000\) \([2, 2]\) \(2654208\) \(3.0679\)  
35280.bj4 35280dy3 \([0, 0, 0, -18917283, 31669112482]\) \(2131200347946769/2058000\) \(722971349065728000\) \([2]\) \(1327104\) \(2.7213\)  
35280.bj5 35280dy2 \([0, 0, 0, -2547363, -1549971038]\) \(5203798902289/57153600\) \(20077947179768217600\) \([2, 2]\) \(884736\) \(2.5186\)  
35280.bj6 35280dy4 \([0, 0, 0, -571683, -3892732382]\) \(-58818484369/18600435000\) \(-6534296202701352960000\) \([2]\) \(1769472\) \(2.8651\)  
35280.bj7 35280dy1 \([0, 0, 0, -289443, 21089698]\) \(7633736209/3870720\) \(1359776316936683520\) \([2]\) \(442368\) \(2.1720\) \(\Gamma_0(N)\)-optimal
35280.bj8 35280dy7 \([0, 0, 0, 5143677, 104935723522]\) \(42841933504271/13565917968750\) \(-4765680279486000000000000\) \([2]\) \(5308416\) \(3.4144\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35280.2.a.bj

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.