Properties

Label 122034i
Number of curves $1$
Conductor $122034$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 122034i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122034.i1 122034i1 \([1, 0, 0, -50886, -5442096]\) \(-2305199161/686796\) \(-4341486856601004\) \([]\) \(620928\) \(1.7149\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122034i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 122034i do not have complex multiplication.

Modular form 122034.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - 4 q^{13} + q^{14} - q^{15} + q^{16} + 3 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display