Properties

Label 116281a
Number of curves $2$
Conductor $116281$
CM \(\Q(\sqrt{-11}) \)
Rank $0$
Graph

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

Elliptic curves in class 116281a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
116281.b2 116281a1 \([0, 1, 1, -7047, -235988]\) \(-32768\) \(-1181267399411\) \([]\) \(119880\) \(1.0939\) \(\Gamma_0(N)\)-optimal \(-11\)
116281.b1 116281a2 \([0, 1, 1, -852727, 310688835]\) \(-32768\) \(-2092687255367950571\) \([]\) \(1318680\) \(2.2929\)   \(-11\)

Rank

sage: E.rank()
 

The elliptic curves in class 116281a have rank \(0\).

Complex multiplication

Each elliptic curve in class 116281a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 116281.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{9} - 2 q^{12} - 3 q^{15} + 4 q^{16} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.