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Properties

Label 3822.a
Number of curves $3$
Conductor $3822$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.a1 3822f3 \([1, 1, 0, -1276769, 554763189]\) \(-1956469094246217097/36641439744\) \(-4310828744441856\) \([]\) \(93312\) \(2.1244\)  
3822.a2 3822f2 \([1, 1, 0, -5954, 1691124]\) \(-198461344537/10417365504\) \(-1225592634180096\) \([]\) \(31104\) \(1.5751\)  
3822.a3 3822f1 \([1, 1, 0, 661, -61851]\) \(270840023/14329224\) \(-1685818874376\) \([]\) \(10368\) \(1.0258\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3822.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{8} + q^{9} + 3 q^{10} + 3 q^{11} - q^{12} - q^{13} + 3 q^{15} + q^{16} + 3 q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.