Properties

Label 6027.c
Number of curves $1$
Conductor $6027$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 6027.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6027.c1 6027d1 \([1, 1, 1, -344, -5146]\) \(-38272753/69741\) \(-8204958909\) \([]\) \(3840\) \(0.59243\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6027.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6027.c do not have complex multiplication.

Modular form 6027.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + q^{9} - 3 q^{10} - 2 q^{11} + q^{12} - 5 q^{13} - 3 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display