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Properties

Label 122010bk
Number of curves $2$
Conductor $122010$
CM no
Rank $1$
Graph

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

Elliptic curves in class 122010bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.bm1 122010bk1 \([1, 1, 1, -15315765361, 729545481167663]\) \(-68921624431417353829938395089/117227740275188640\) \(-675794594366147747060640\) \([]\) \(146200320\) \(4.2621\) \(\Gamma_0(N)\)-optimal
122010.bm2 122010bk2 \([1, 1, 1, 47775808989, 3865873444570689]\) \(2092008964199791878427102647311/2330581636033743421440000000\) \(-13435339345988960109660733440000000\) \([]\) \(1023402240\) \(5.2351\)  

Rank

sage: E.rank()
 

The elliptic curves in class 122010bk have rank \(1\).

Complex multiplication

The elliptic curves in class 122010bk do not have complex multiplication.

Modular form 122010.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 2 q^{11} - q^{12} + q^{15} + q^{16} + 3 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.