Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3822.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.w1 3822v2 \([1, 1, 1, -180050305, 929830670369]\) \(-5486773802537974663600129/2635437714\) \(-310056611614386\) \([]\) \(395136\) \(3.0195\)  
3822.w2 3822v1 \([1, 1, 1, 34985, 28472429]\) \(40251338884511/2997011332224\) \(-352595386224821376\) \([]\) \(56448\) \(2.0465\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3822.2.a.w

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.