Properties

Label 975.b
Number of curves $1$
Conductor $975$
CM no
Rank $1$

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

Elliptic curves in class 975.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
975.b1 975b1 \([0, -1, 1, -8, -82]\) \(-4096/195\) \(-3046875\) \([]\) \(288\) \(-0.075866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 975.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 975.b do not have complex multiplication.

Modular form 975.2.a.b

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