Properties

Label 25050e
Number of curves $1$
Conductor $25050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 25050e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25050.a1 25050e1 \([1, 1, 0, -7575, -1762875]\) \(-24616775429/670674672\) \(-1309911468750000\) \([]\) \(234240\) \(1.5813\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 25050e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 25050e do not have complex multiplication.

Modular form 25050.2.a.e

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