Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3870r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3870.o2 3870r1 \([1, -1, 1, -338, -1519]\) \(5841725401/1857600\) \(1354190400\) \([2]\) \(2304\) \(0.45604\) \(\Gamma_0(N)\)-optimal
3870.o1 3870r2 \([1, -1, 1, -2138, 37361]\) \(1481933914201/53916840\) \(39305376360\) \([2]\) \(4608\) \(0.80261\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3870.2.a.r

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