Properties

Label 19074bh
Number of curves $4$
Conductor $19074$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 19074bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19074.bd4 19074bh1 \([1, 0, 0, -584, 48]\) \(912673/528\) \(12744636432\) \([2]\) \(20480\) \(0.62851\) \(\Gamma_0(N)\)-optimal
19074.bd2 19074bh2 \([1, 0, 0, -6364, -195316]\) \(1180932193/4356\) \(105143250564\) \([2, 2]\) \(40960\) \(0.97508\)  
19074.bd1 19074bh3 \([1, 0, 0, -101734, -12498046]\) \(4824238966273/66\) \(1593079554\) \([2]\) \(81920\) \(1.3217\)  
19074.bd3 19074bh4 \([1, 0, 0, -3474, -372762]\) \(-192100033/2371842\) \(-57250499932098\) \([2]\) \(81920\) \(1.3217\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19074bh have rank \(0\).

Complex multiplication

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

Modular form 19074.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} - 2 q^{10} + q^{11} + q^{12} - 6 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.