Properties

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

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

Elliptic curves in class 3675.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.k1 3675g1 \([1, 1, 0, -200, 3375]\) \(-46585/243\) \(-4651171875\) \([]\) \(1800\) \(0.53927\) \(\Gamma_0(N)\)-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)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 3 q^{8} + q^{9} + q^{12} + 3 q^{13} - q^{16} - 2 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display