Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 8400.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.ch1 8400cr1 \([0, 1, 0, -7208, -230412]\) \(5177717/189\) \(1512000000000\) \([2]\) \(15360\) \(1.1066\) \(\Gamma_0(N)\)-optimal
8400.ch2 8400cr2 \([0, 1, 0, 2792, -810412]\) \(300763/35721\) \(-285768000000000\) \([2]\) \(30720\) \(1.4532\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8400.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 6 q^{11} + 2 q^{13} - 4 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.