Properties

Label 92400.e
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.e1 92400g4 \([0, -1, 0, -206008, -35919488]\) \(60430765429444/2525985\) \(40415760000000\) \([2]\) \(589824\) \(1.6915\)  
92400.e2 92400g3 \([0, -1, 0, -63008, 5638512]\) \(1729010797924/148561875\) \(2376990000000000\) \([2]\) \(589824\) \(1.6915\)  
92400.e3 92400g2 \([0, -1, 0, -13508, -499488]\) \(68150496976/12006225\) \(48024900000000\) \([2, 2]\) \(294912\) \(1.3449\)  
92400.e4 92400g1 \([0, -1, 0, 1617, -45738]\) \(1869154304/4611915\) \(-1152978750000\) \([2]\) \(147456\) \(0.99831\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.e have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.e do not have complex multiplication.

Modular form 92400.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.