Properties

Label 3675.k
Number of curves $1$
Conductor $3675$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3675.k1 3675g1 [1, 1, 0, -200, 3375] [] 1800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3675.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3675.k do not have complex multiplication.

Modular form 3675.2.a.k

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