Properties

Label 425.b
Number of curves $1$
Conductor $425$
CM no
Rank $1$

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

Elliptic curves in class 425.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
425.b1 425c1 \([1, 0, 0, -3, 2]\) \(-121945/17\) \(-425\) \([]\) \(12\) \(-0.76419\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 425.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 425.b do not have complex multiplication.

Modular form 425.2.a.b

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