Properties

Label 3870i
Number of curves $2$
Conductor $3870$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3870i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3870.g2 3870i1 [1, -1, 0, -92304, 11216128] [2] 40320 \(\Gamma_0(N)\)-optimal
3870.g1 3870i2 [1, -1, 0, -1491984, 701818240] [2] 80640  

Rank

sage: E.rank()
 

The elliptic curves in class 3870i have rank \(1\).

Complex multiplication

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

Modular form 3870.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - 4q^{7} - q^{8} - q^{10} + 4q^{11} + 4q^{13} + 4q^{14} + q^{16} - 4q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.