Properties

Label 6003.c
Number of curves $1$
Conductor $6003$
CM no
Rank $1$

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

Elliptic curves in class 6003.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6003.c1 6003c1 \([1, -1, 0, 99, 1498]\) \(146363183/1458729\) \(-1063413441\) \([]\) \(2240\) \(0.41319\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6003.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6003.c do not have complex multiplication.

Modular form 6003.2.a.c

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