Properties

Label 123210.f
Number of curves $1$
Conductor $123210$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 123210.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123210.f1 123210c1 \([1, -1, 0, 141435, 7415381]\) \(4516672077/2960000\) \(-205052854607280000\) \([]\) \(1225728\) \(2.0107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123210.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 123210.f do not have complex multiplication.

Modular form 123210.2.a.f

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