Properties

Label 12480bl
Number of curves $6$
Conductor $12480$
CM no
Rank $0$
Graph

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

Elliptic curves in class 12480bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.o6 12480bl1 \([0, -1, 0, 959, -4895]\) \(371694959/249600\) \(-65431142400\) \([2]\) \(12288\) \(0.76407\) \(\Gamma_0(N)\)-optimal
12480.o5 12480bl2 \([0, -1, 0, -4161, -36639]\) \(30400540561/15210000\) \(3987210240000\) \([2, 2]\) \(24576\) \(1.1106\)  
12480.o2 12480bl3 \([0, -1, 0, -54081, -4818975]\) \(66730743078481/60937500\) \(15974400000000\) \([2]\) \(49152\) \(1.4572\)  
12480.o3 12480bl4 \([0, -1, 0, -36161, 2632161]\) \(19948814692561/231344100\) \(60645467750400\) \([2, 2]\) \(49152\) \(1.4572\)  
12480.o1 12480bl5 \([0, -1, 0, -576961, 168874081]\) \(81025909800741361/11088090\) \(2906676264960\) \([2]\) \(98304\) \(1.8038\)  
12480.o4 12480bl6 \([0, -1, 0, -7361, 6681441]\) \(-168288035761/73415764890\) \(-19245502271324160\) \([2]\) \(98304\) \(1.8038\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12480bl have rank \(0\).

Complex multiplication

The elliptic curves in class 12480bl do not have complex multiplication.

Modular form 12480.2.a.bl

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