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Properties

Label 19602.p
Number of curves $2$
Conductor $19602$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 19602.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19602.p1 19602l2 \([1, -1, 0, -6738, 234152]\) \(-35937/4\) \(-3765920597604\) \([]\) \(51840\) \(1.1504\)  
19602.p2 19602l1 \([1, -1, 0, 522, -588]\) \(109503/64\) \(-9183772224\) \([]\) \(17280\) \(0.60114\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19602.p have rank \(0\).

Complex multiplication

The elliptic curves in class 19602.p do not have complex multiplication.

Modular form 19602.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.