Properties

Label 847.a
Number of curves $2$
Conductor $847$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 847.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
847.a1 847c2 \([1, 1, 1, -6234, -177484]\) \(15124197817/1294139\) \(2292646180979\) \([2]\) \(1440\) \(1.1129\)  
847.a2 847c1 \([1, 1, 1, 421, -12440]\) \(4657463/41503\) \(-73525096183\) \([2]\) \(720\) \(0.76635\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 847.a have rank \(1\).

Complex multiplication

The elliptic curves in class 847.a do not have complex multiplication.

Modular form 847.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} - q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 2 q^{12} - 4 q^{13} - q^{14} - 4 q^{15} - q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.