Properties

Label 19481.e
Number of curves $4$
Conductor $19481$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 19481.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19481.e1 19481b3 \([1, -1, 0, -14966, -700815]\) \(209267191953/55223\) \(97830913103\) \([2]\) \(25600\) \(1.0933\)  
19481.e2 19481b2 \([1, -1, 0, -1051, -7848]\) \(72511713/25921\) \(45920632681\) \([2, 2]\) \(12800\) \(0.74674\)  
19481.e3 19481b1 \([1, -1, 0, -446, 3647]\) \(5545233/161\) \(285221321\) \([2]\) \(6400\) \(0.40017\) \(\Gamma_0(N)\)-optimal
19481.e4 19481b4 \([1, -1, 0, 3184, -57821]\) \(2014698447/1958887\) \(-3470287812607\) \([2]\) \(25600\) \(1.0933\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19481.e have rank \(0\).

Complex multiplication

The elliptic curves in class 19481.e do not have complex multiplication.

Modular form 19481.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2 q^{5} - q^{7} - 3 q^{8} - 3 q^{9} + 2 q^{10} - 6 q^{13} - q^{14} - q^{16} + 2 q^{17} - 3 q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.