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Properties

Label 122010u
Number of curves $2$
Conductor $122010$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 122010u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.r1 122010u1 \([1, 0, 1, -4768286410074, -3965581960364722484]\) \(101911330862444537650467942170606186761/1232143448888598218129390625000000\) \(144960444618294691764704677640625000000\) \([2]\) \(6386688000\) \(6.1334\) \(\Gamma_0(N)\)-optimal
122010.r2 122010u2 \([1, 0, 1, -892725993794, -10225390245188511508]\) \(-668790373670946788154751785606988681/383545828061955844402313232421875000\) \(-45123783125661043138087749481201171875000\) \([2]\) \(12773376000\) \(6.4799\)  

Rank

sage: E.rank()
 

The elliptic curves in class 122010u have rank \(0\).

Complex multiplication

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

Modular form 122010.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 2 q^{13} - q^{15} + q^{16} - 8 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.