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Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 3870.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3870.f1 3870h1 \([1, -1, 0, -1719, -24867]\) \(770842973809/66873600\) \(48750854400\) \([2]\) \(5120\) \(0.79160\) \(\Gamma_0(N)\)-optimal
3870.f2 3870h2 \([1, -1, 0, 1881, -117747]\) \(1009328859791/8734528080\) \(-6367470970320\) \([2]\) \(10240\) \(1.1382\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3870.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - 4 q^{7} - q^{8} - q^{10} + 2 q^{11} - 6 q^{13} + 4 q^{14} + q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.