Properties

Label 250470x
Number of curves $1$
Conductor $250470$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 250470x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250470.x1 250470x1 \([1, -1, 0, -1677330, 836553460]\) \(5916522263654774761/134323680\) \(11848557489120\) \([]\) \(2887680\) \(2.0325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250470x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250470x do not have complex multiplication.

Modular form 250470.2.a.x

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