Properties

Label 8400.o
Number of curves $2$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.o1 8400bx2 \([0, -1, 0, -1708, 24412]\) \(1102736/147\) \(73500000000\) \([2]\) \(7680\) \(0.81273\)  
8400.o2 8400bx1 \([0, -1, 0, 167, 1912]\) \(16384/63\) \(-1968750000\) \([2]\) \(3840\) \(0.46616\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8400.o have rank \(0\).

Complex multiplication

The elliptic curves in class 8400.o do not have complex multiplication.

Modular form 8400.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.