Properties

Label 94864.bk
Number of curves $2$
Conductor $94864$
CM \(\Q(\sqrt{-11}) \)
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 94864.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
94864.bk1 94864bt2 \([0, -1, 0, -695669, -228913859]\) \(-32768\) \(-1136272129632088064\) \([]\) \(1216512\) \(2.2420\)   \(-11\)
94864.bk2 94864bt1 \([0, -1, 0, -5749, 174077]\) \(-32768\) \(-641395994624\) \([]\) \(110592\) \(1.0430\) \(\Gamma_0(N)\)-optimal \(-11\)

Rank

sage: E.rank()
 

The elliptic curves in class 94864.bk have rank \(1\).

Complex multiplication

Each elliptic curve in class 94864.bk has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 94864.2.a.bk

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