Properties

Label 15210bn
Number of curves $6$
Conductor $15210$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15210bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bq6 15210bn1 \([1, -1, 1, 22783, -535791]\) \(371694959/249600\) \(-878278442745600\) \([4]\) \(86016\) \(1.5561\) \(\Gamma_0(N)\)-optimal
15210.bq5 15210bn2 \([1, -1, 1, -98897, -4380879]\) \(30400540561/15210000\) \(53520092604810000\) \([2, 2]\) \(172032\) \(1.9027\)  
15210.bq2 15210bn3 \([1, -1, 1, -1285277, -560081271]\) \(66730743078481/60937500\) \(214423447935937500\) \([2]\) \(344064\) \(2.2493\)  
15210.bq3 15210bn4 \([1, -1, 1, -859397, 303773721]\) \(19948814692561/231344100\) \(814040608519160100\) \([2, 2]\) \(344064\) \(2.2493\)  
15210.bq1 15210bn5 \([1, -1, 1, -13711847, 19546461861]\) \(81025909800741361/11088090\) \(39016147508906490\) \([2]\) \(688128\) \(2.5959\)  
15210.bq4 15210bn6 \([1, -1, 1, -174947, 773853981]\) \(-168288035761/73415764890\) \(-258331264665730351290\) \([2]\) \(688128\) \(2.5959\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15210bn have rank \(0\).

Complex multiplication

The elliptic curves in class 15210bn do not have complex multiplication.

Modular form 15210.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.