Properties

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

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

Elliptic curves in class 4025.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.b1 4025e1 \([0, 1, 1, 575092, 300275344]\) \(1346216501445963776/3268768272021875\) \(-51074504250341796875\) \([]\) \(137280\) \(2.4656\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4025.b1 has rank \(1\).

Complex multiplication

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

Modular form 4025.2.a.b

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