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Properties

Label 42050bh
Number of curves $4$
Conductor $42050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 42050bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42050.x3 42050bh1 \([1, 1, 1, -438, -41819]\) \(-25/2\) \(-743529151250\) \([]\) \(50400\) \(0.95755\) \(\Gamma_0(N)\)-optimal
42050.x1 42050bh2 \([1, 1, 1, -105563, -13245519]\) \(-349938025/8\) \(-2974116605000\) \([]\) \(151200\) \(1.5069\)  
42050.x2 42050bh3 \([1, 1, 1, -63513, 7401031]\) \(-121945/32\) \(-7435291512500000\) \([]\) \(252000\) \(1.7623\)  
42050.x4 42050bh4 \([1, 1, 1, 462112, -54622719]\) \(46969655/32768\) \(-7613738508800000000\) \([]\) \(756000\) \(2.3116\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42050bh have rank \(1\).

Complex multiplication

The elliptic curves in class 42050bh do not have complex multiplication.

Modular form 42050.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + q^{16} + 3 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.