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Properties

Label 19074.s
Number of curves $2$
Conductor $19074$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 19074.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19074.s1 19074s1 \([1, 1, 1, -104913, -12939105]\) \(1076890625/17424\) \(2066275160083728\) \([2]\) \(104448\) \(1.7383\) \(\Gamma_0(N)\)-optimal
19074.s2 19074s2 \([1, 1, 1, -6653, -36089161]\) \(-274625/4743684\) \(-562543412332794948\) \([2]\) \(208896\) \(2.0848\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19074.s have rank \(1\).

Complex multiplication

The elliptic curves in class 19074.s do not have complex multiplication.

Modular form 19074.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + q^{11} - q^{12} + 2 q^{13} + q^{16} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.