Properties

Label 4025.a
Number of curves $1$
Conductor $4025$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 4025.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.a1 4025d1 \([0, 0, 1, -325, 6156]\) \(-242970624/907235\) \(-14175546875\) \([]\) \(8640\) \(0.63357\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4025.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 4025.a do not have complex multiplication.

Modular form 4025.2.a.a

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