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Properties

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

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

Elliptic curves in class 3822.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.bh1 3822bc1 \([1, 0, 0, -1079, 25857]\) \(-24100657/36504\) \(-210438295704\) \([3]\) \(7056\) \(0.86432\) \(\Gamma_0(N)\)-optimal
3822.bh2 3822bc2 \([1, 0, 0, 9211, -519513]\) \(14991903983/28960854\) \(-166953560100054\) \([]\) \(21168\) \(1.4136\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3822.2.a.bh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.