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Properties

Label 3822.b
Number of curves $2$
Conductor $3822$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.b1 3822e1 \([1, 1, 0, -58741, -1282259]\) \(65352943209688399/35827476332544\) \(12288824382062592\) \([2]\) \(37440\) \(1.7780\) \(\Gamma_0(N)\)-optimal
3822.b2 3822e2 \([1, 1, 0, 227979, -9826515]\) \(3820420340137317041/2334869460099072\) \(-800860224813981696\) \([2]\) \(74880\) \(2.1246\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3822.b have rank \(0\).

Complex multiplication

The elliptic curves in class 3822.b do not have complex multiplication.

Modular form 3822.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} - q^{12} - q^{13} + 2 q^{15} + q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 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.