Properties

Label 8400.a
Number of curves $2$
Conductor $8400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.a1 8400br2 \([0, -1, 0, -5608, 172912]\) \(-7620530425/526848\) \(-1348730880000\) \([]\) \(15552\) \(1.0785\)  
8400.a2 8400br1 \([0, -1, 0, 392, 112]\) \(2595575/1512\) \(-3870720000\) \([]\) \(5184\) \(0.52916\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8400.a have rank \(1\).

Complex multiplication

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

Modular form 8400.2.a.a

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.