Properties

Label 283920.bl
Number of curves $8$
Conductor $283920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.bl1 283920bl7 \([0, -1, 0, -949732736, 11265810186240]\) \(4791901410190533590281/41160000\) \(813758293770240000\) \([2]\) \(63700992\) \(3.4779\)  
283920.bl2 283920bl6 \([0, -1, 0, -59359616, 176034902016]\) \(1169975873419524361/108425318400\) \(2143634647781317017600\) \([2, 2]\) \(31850496\) \(3.1313\)  
283920.bl3 283920bl8 \([0, -1, 0, -55033216, 202778976256]\) \(-932348627918877961/358766164249920\) \(-7093025794035679663226880\) \([2]\) \(63700992\) \(3.4779\)  
283920.bl4 283920bl4 \([0, -1, 0, -11782736, 15297666240]\) \(9150443179640281/184570312500\) \(3649067604000000000000\) \([2]\) \(21233664\) \(2.9286\)  
283920.bl5 283920bl3 \([0, -1, 0, -3981696, 2325442560]\) \(353108405631241/86318776320\) \(1706574833296846356480\) \([2]\) \(15925248\) \(2.7847\)  
283920.bl6 283920bl2 \([0, -1, 0, -1561616, -393797184]\) \(21302308926361/8930250000\) \(176556486951936000000\) \([2, 2]\) \(10616832\) \(2.5820\)  
283920.bl7 283920bl1 \([0, -1, 0, -1345296, -599906880]\) \(13619385906841/6048000\) \(119572647247872000\) \([2]\) \(5308416\) \(2.2354\) \(\Gamma_0(N)\)-optimal
283920.bl8 283920bl5 \([0, -1, 0, 5198384, -2897701184]\) \(785793873833639/637994920500\) \(-12613548540820211712000\) \([2]\) \(21233664\) \(2.9286\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 283920.bl do not have complex multiplication.

Modular form 283920.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.