Properties

Label 53900.e
Number of curves $4$
Conductor $53900$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 53900.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53900.e1 53900v4 \([0, 1, 0, -240271908, 1431989153188]\) \(3259751350395879376/3806353980275\) \(1791254957701493900000000\) \([2]\) \(11943936\) \(3.5659\)  
53900.e2 53900v3 \([0, 1, 0, -240204533, 1432833227188]\) \(52112158467655991296/71177645\) \(2093494689151250000\) \([2]\) \(5971968\) \(3.2193\)  
53900.e3 53900v2 \([0, 1, 0, -11196908, -12396096812]\) \(329890530231376/49933296875\) \(23498409776187500000000\) \([2]\) \(3981312\) \(3.0166\)  
53900.e4 53900v1 \([0, 1, 0, -3044533, 1854254688]\) \(106110329552896/10850811125\) \(319146769511281250000\) \([2]\) \(1990656\) \(2.6700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53900.e have rank \(0\).

Complex multiplication

The elliptic curves in class 53900.e do not have complex multiplication.

Modular form 53900.2.a.e

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.