Properties

Label 412224r
Number of curves $1$
Conductor $412224$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 412224r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.r1 412224r1 \([0, -1, 0, -8815, 336289]\) \(-1183749898530304/65037218139\) \(-4162381960896\) \([]\) \(622336\) \(1.1794\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 412224r do not have complex multiplication.

Modular form 412224.2.a.r

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