Properties

Label 3870y
Number of curves $4$
Conductor $3870$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3870y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3870.z3 3870y1 [1, -1, 1, -617, 6041] [4] 1536 \(\Gamma_0(N)\)-optimal
3870.z2 3870y2 [1, -1, 1, -797, 2369] [2, 2] 3072  
3870.z1 3870y3 [1, -1, 1, -7547, -248731] [2] 6144  
3870.z4 3870y4 [1, -1, 1, 3073, 16301] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 3870y have rank \(0\).

Complex multiplication

The elliptic curves in class 3870y do not have complex multiplication.

Modular form 3870.2.a.y

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.