Properties

Label 675.b
Number of curves $1$
Conductor $675$
CM no
Rank $1$

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

Elliptic curves in class 675.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
675.b1 675b1 \([1, -1, 1, -5, 2]\) \(1875\) \(6075\) \([]\) \(36\) \(-0.58268\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 675.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 675.b do not have complex multiplication.

Modular form 675.2.a.b

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