Properties

Label 250025b
Number of curves $1$
Conductor $250025$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 250025b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250025.b1 250025b1 \([1, 0, 0, -20088, 1093667]\) \(57374000974009/31253125\) \(488330078125\) \([]\) \(418560\) \(1.1914\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250025b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 250025b do not have complex multiplication.

Modular form 250025.2.a.b

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