Properties

Label 19855.a
Number of curves $4$
Conductor $19855$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 19855.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19855.a1 19855c3 \([1, -1, 1, -367060897, 2381187629246]\) \(116256292809537371612841/15216540068579856875\) \(715875533298139785538281875\) \([2]\) \(6359040\) \(3.8812\)  
19855.a2 19855c2 \([1, -1, 1, -354651522, 2570738350496]\) \(104859453317683374662841/2223652969140625\) \(104613712971486516015625\) \([2, 2]\) \(3179520\) \(3.5346\)  
19855.a3 19855c1 \([1, -1, 1, -354649717, 2570765825484]\) \(104857852278310619039721/47155625\) \(2218477922230625\) \([4]\) \(1589760\) \(3.1880\) \(\Gamma_0(N)\)-optimal
19855.a4 19855c4 \([1, -1, 1, -342271027, 2758530650854]\) \(-94256762600623910012361/15323275604248046875\) \(-720897000607656707763671875\) \([2]\) \(6359040\) \(3.8812\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19855.a have rank \(1\).

Complex multiplication

The elliptic curves in class 19855.a do not have complex multiplication.

Modular form 19855.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{8} - 3 q^{9} - q^{10} - q^{11} - 2 q^{13} - q^{16} - 6 q^{17} + 3 q^{18} + O(q^{20})\) 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.