Properties

Label 184041.q
Number of curves $2$
Conductor $184041$
CM \(\Q(\sqrt{-11}) \)
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 184041.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
184041.q1 184041o2 \([0, 0, 1, -1349634, 619200832]\) \(-32768\) \(-8297013726470605851\) \([]\) \(3104640\) \(2.4077\)   \(-11\)
184041.q2 184041o1 \([0, 0, 1, -11154, -465215]\) \(-32768\) \(-4683447945891\) \([]\) \(282240\) \(1.2087\) \(\Gamma_0(N)\)-optimal \(-11\)

Rank

sage: E.rank()
 

The elliptic curves in class 184041.q have rank \(2\).

Complex multiplication

Each elliptic curve in class 184041.q has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 184041.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 3 q^{5} + 4 q^{16} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.